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If a + B + C = 9 and Ab + Bc + Ca = 40, Find A2 + B2 +C2. - Mathematics

Answer in Brief

If a + b + c = 9 and ab + bc + ca = 40, find a2 + b2 +c2.

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Solution

Recall the formula

 `(a+b+c)^2 = a^2 +b^2 +c^2 +2(ab +bc+ca)`

Given that

  `(a+b+c) = 9,ab + bc + ca = 40`

Then we have

`(a+b+c)^2 = a^2 + b^2 + c^2 + 2(ab + bc + ca)`

` ( 9)^2 = a^2 + b^2 + c^2  + 2.( 40) `

`a^2 ++ b^2 + c^2 + 80 = 81` 

        `a^2 + b^2 + c^2 = 81 - 80

                `a^2 + b^2 +c^2 =` 1

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APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 5 Factorisation of Algebraic Expressions
Q 3 | Page 24
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