In this this video we are going to show the proof of one more fundamental identity of algebraIt states that (abc)²=a²b²c²2(abbcca)To derive thisIf `abc=9` and `abbcca=26`, find the value of `a^2b^2c^2`b2 =(a−b)22ab 3 (a b c)2 = a2 b2 c2 2(ab bc ca) 4 (a b) 3= a3 b3 3ab(a b);
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(ab+bc+ca)^2 formula
(ab+bc+ca)^2 formula-= a 2 ab ac ba b 2 bc ca cb c 2 Adding like terms, the final formula (worth remembering) is (a b c) 2 = a 2 b 2 c 2 2ab 2bc 2ac Practice Exercise for Algebra Module on Expansion of (a b c)The area of the ΔABC can be calculated using Heron's formula S = (AB BC AC)/2 = (10 17 21)/2 = 24 cm = √ 24(24 10) (24 17) (24 21) = 84 cm2 Step 5 Similarly, the area of the ΔACD can be calculated using Heron's formula S = (AC CD AD)/2 = (21 13 )/2 = 27 cm
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Given that, a 2 b 2 c 2 = 50 and a b c = 12 We need to find ab bc ca Substitute the values of (a 2 b 2 c 2 ) and ( a b c ) in the identity (1), we have (12) 2 = 50 2 ( ab bc ca ) ⇒ 144 = 50 2 ( ab bc ca ) ⇒ 94 = 2 ( ab bc ca) ⇒ ab bc ca = `94/2` ⇒ ab bc caSocratic =>v=2ab2ca2bc =>2ab2ca=v2bc =>2a(bc)=v2bc =>a=(v2bc)/((2(bc)) Algebra Given v= 2(ab bc ca), how do you solve for a?
Section Formula With Examples Type I On finding the section point when the section ratio is given Example 1 Find the coordinates of the point which divides the line segment joining the points (6, 3) and (– 4, 5) in the ratio 3 2 internally Sol Let P (x, y) be the required pointb2 =(ab)2−2ab 2 (a−b)2 = a 2−2ab b; Get the list of basic algebra formulas in Maths at BYJU'S Stay tuned with BYJU'S to get all the important formulas in various chapters like trigonometry, probability and so on
SolutionShow Solution a 2 b 2 c 2 = 50 and ab bc ca = 47 Since ( a b c ) 2 = a 2 b 2 c 2 2 ( ab bc ca ) ∴ ( a b c ) 2 = 50 2 (47) ⇒ ( a b c ) 2 = 50 94 = 144 ⇒ a b c = `sqrt144 = 12` ∴ a b c = `12` Concept Expansion of Formula1 (a b)2 = a2 2ab b2;Click here👆to get an answer to your question ️ If a^2 b^2 c^2 ab bc ca = 0 , prove that a = b = c
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The area of whole square is ( a b c) 2 geometrically The whole square is split as three squares and six rectangles So, the area of whole square is equal to the sum of the areas of three squares and six rectangles ( a b c) 2 = a 2 a b c a a b b 2 b c c a b c c 2 Now, simplify the expansion of the a b c wholeA 2 b 2 c 2 2ab 2bc 2ca = 625 a 2 b 2 c 2 2 (ab bc ca) = 625 a 2 b 2 c 2 2 × 59 = 625 Given, ab bc ca = 59 a 2 b 2 c 2 118 = 625 a 2 b 2 c 2 118 – 118 = 625 – 118 subtracting 118 from both the sides Therefore, a 2 b 2 c 2 = 507If a = 1001, b = 1002, c = 1003 , then value of a2 b2 c2 – ab – bc – ca isIn this video, we will understand short trick of Algebraic expressions a^2
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A plus b minus c Whole Square Formula To get formula / expansion for (a b c) 2, let us consider the formula / expansion for (a b c) 2 The formula or expansion for (a b c) 2 is (a b c) 2 = a 2 b 2 c 2 2ab 2bc 2ac In (a b c) 2, if c is negative, then we have (a b c) 2 In the terms of the expansion for (a b c) 2, consider the terms in which we find "c"You can check the formulas of A plus B plus C Whole cube in three ways We are going to share the (abc)^3 algebra formulas for you as well as how to create (abc)^3 and proof we can write we know that what is the formula of need too write in simple form of multiplication Simplify the all Multiplication one by oneUsing the 1/b 1/c = 2 and abc = 3 Solution To find a 2 b 2 c 2 Given that
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The actual formula is (abc)² = a² b² c² 2 (ab bc ca) You can get this simple formula by multiplying (ab c) with (abc) (ab c)² = (ab c)* (ab c)Summary (abc)^2 If you have any issues in the (abc)^2 formulas, please let me know through social media and mail A Plus B Plus C Whole Square isClick here👆to get an answer to your question ️ Write the following in the expanded form (ab bc ca)^2
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Consider, a2 b2 c2 – ab – bc – ca = 0 Multiply both sides with 2, we get 2 (a2 b2 c2 – ab – bc – ca) = 0 ⇒ 2a2 2b2 2c2 – 2ab – 2bc – 2ca = 0 2 Answers2 Active Oldest Votes 2 If a, b, and c are required to only be positive integers and some of them is 1, then we have a unique solution ( a, b, c) = ( 1, 1, 1) For solutions with a, b, c > 1, note that ( a − 1) ( b − 1) ( c − 1) = a b c − b c − c a − a b a b c − 1 = a b c − 3 Set x = a − 1, y = b −(abbcca)^2 formulaThe Health Gateway is a Ministry of Health initiative which provides BC residents and their families with secure access to a single view of their health information View and download your health information, such as COVID19 tests, COVID19 immunizations, medications, immunizations and health visitsEx 42, 7 By using properties of determinants, show that 8(−a2&ab
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Subhikshasampath (abc) 2 =a 2 b 2 c 2 2ab2bc2ca a 2 b 2 c 2 = (abc) 2 2ab2bc2ca a 2 b 2 c 2 = (7) 2 2 (abbcca) a 2 b 2 c 2 = (7) 2 2 () a 2 b 2 c 2 = 4940 a2b2c2= 9 There are various student are search formula of (ab)^3 and a^3b^3 Now I am going to explain everything below You can check and revert back if you like you can also check cube formula in algebra formula sheet a2 – b2 = (a – b)(a b) (ab)2 = a2 2ab b2 a2 b2 = (a –For more Questions Subscribe our Channel https//youtubecom/c/GRAVITYCOACHINGCENTRE?sub_confirmation=1
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Ab, V bc, and V ca (or phase voltages) into two symmetrical componentsV p andV n (of the line or phase voltages) The two balanced components are given by V VaV aV p = ab bc ca ⋅ ⋅2 3 (4) V VaV aV n = ab bc ca ⋅ ⋅2 3 (5) where aa=∠ ° =∠ °1 1 1 240and 2 The positive and negative sequence voltages can be used when ana Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers Visit Stack ExchangeTriangular prism Volume and surface area of Triangular prism A prism with the triangle as the base is called triangular prism In the case of a triangular prism, two congruent and parallel triangles ABC and EFG are called the base of the prism
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Click here👆to get an answer to your question ️ If a b c = 9 and ab bc ca = 26 , then find a^2 b^2 c^2Given that, a 2 b 2 c 2 = 35 and ab bc ca = 23 We need to find a b c Substitute the values of ( a 2 b 2 c 2 ) and ( ab bc ca ) in the identity (1), we have ( a b c ) 2 = 35 2 (23) ⇒ ( a b c ) 2 = 81 ⇒ a b c = `sqrt81` ⇒ a b c = `9` Concept Expansion of FormulaA3 −b3 =(a−b)33ab(a−b) 6 a2 −b2 =(ab)(a−b) 7 a3 −b3 =(a−b)(a2 ab b2) 8 a3 b3 =(ab)(a2 −ab b2) 9 a n−bn=(a−b)(an−1 a −2b an−3b2
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If A 2 B 2 C 2 Ab Ca 0 A B C In R Then Find The Value Of The Determinant A B 2 2 A 2 B 2 1 1 B C 2 2 B 2 C 2 C 2 A 2 1 C A 2 2 A Abc A 2 B 2 C 2
X³ (abc) x² (abbcca) xabc a² b² c² a b b c c a = ½ (ab)²(bc)²(ca)² (abc) (a² b² c² a bb cc a) = a³ b³ c³ 3 a b c Logarithms Math Formulas Product rule log ₐ (m n) = log ₐ m log ₐ nA² b² c² = (a b c)² 2 (ab bc ca)Wwwsakshieducationcom wwwsakshieducationcom 2 22 cos 2 ab c c ab − = ∴ 2bc 22 2 2 bc a bc − 2ac 22 2 2 ac b ac − 2ab 222 2 abc ab 22bc − a 2 a2 −cb22 a2 b2 − c = abc22 2 8 Prove that 222 22 2
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(a b c) 2 = a 2 b 2 c 2 2 (a b b c c a) The LHS of the above identity is a perfect square, hence it is always positive or 0 As stated in the title, I'm supposed to show that $(abc)^3 = a^3 b^3 c^3 (abc)(abacbc)$ My reasoning $$(a b c)^3 = (a b) c^3 = (a b)^3 3(a b)^2c 3(a b)c^2 c^3 Stack Exchange network consists of 178 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share theirA3 b3 =(ab)−3ab(a b) 5 (a−b)3 = a3 −b3 −3ab(a−b);
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Where k is any integer (since net coefficients are integers) Now ((a2 b2 c2) k (ab bc ca) ) (abc) = a3b3c3−3abc The value of can be easily found out to be 1 (even by simply multiplying and comparing);Hence the other factor, (a2 b2 c2 ab bc ca) 41K answers 2M people helped The Formula is given below (a b c)³ = a³ b³ c³ 3 (a b) (b c) (a c) Explanation Let us just start with (abc)² = a² b² c²2ab2bc2ca =a² b² c²2 (abbcca) now
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Answer The required formula is Stepbystep explanation We are given to find the formula for the following expression We know that if x, y and z are any three real numbers, then the following identity holds Therefore, we get Thus, the required formula is taffy927x2 and 191 more users found this answer helpful heart outlined(ABBCCA)^2 =(ABBCCA)(ABBCCA) =(AB)^2AB^2CA^2BCAB^2C(BC)^2ABC^2A^2BCABC^2(CA)^2 =(AB)^2(BC)^2(CA)^22A^2BC2AB^2C2ABC^2 =(AB)^2(BC)^2(CA)^22(A^2BCAB^2CABC^2) =(AB)^2(BC)^2(CA)^22ABC(ABC) (or)Click here👆to get an answer to your question ️ If a b c = 9 and ab bc ca = 23 , then a^2 b^2 c^2 is equal to Join / Login maths If a b c = 9 and a b b c c a = 2 3, then a 2 b 2 c 2 is equal to A 3 5 B 5 8 C 1 2 7 D None of these Answer Correct option is A 3 5 Formula, (a b c) 2 = a 2 b 2 c 2
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Evaluate ( B2 C2 Ab Ca)(A B C) CISCE ICSE Class 7 Textbook Solutions 7008 Question Bank Solutions 6480 Concept Notes & Videos 150 Syllabus Advertisement Remove all ads Evaluate ( B2 C2 Ab Ca)(A B C) Mathematics Hence we have the other factor = (a2 b2 c2) k (ab bc ca) ;Recall the formula ` (abc)^2 = a^2 b^2 c^2 2 (ab bc ca)` Given that `a^2 b^2 c^2 = 250 , ab bc ca = 3 ` Then we have ` (abc)^2 = a^2 b^2 c^2 2 (ab bcca)` ` (abc)^2 = 250 2 (3)` ` (abc)^2 = 256` ` (abc) =± 16`
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Using this formula (abc)² = a² b² c² 2 (ab bc ca)If a^2b^2c^2abbcca=0 then prove that a=b=c Get the answer to this question along with unlimited Maths questions and prepare better for JEE exam
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