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If A + B + C = 9 And Ab + Bc + Ca = 23, Then A2 + B2 + C2 = - Mathematics

MCQ

If a + b + c = 9 and ab + bc + ca = 23, then a2 + b2 + c2 =

Options

  • 35

  • 58

  • 127

  •  none of these

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Solution

We have to find  `a^2 + b^2 + c^2`

Given  `a+b + c = 9,ab+bc +ca  = 23`

Using identity `(a+b+c)^2 = a^2 + b^2 +c^2+2ab + 2bc + 2ca` we get,

`(9)^2 = a^2 +b^2 + c^2+ 2 (ab + bc + ca)`

` 9 xx 9 = a^2 + b^2 + c^2 +2 xx 23`

`81 = a^2 + b^2 + c^2+46`

By transposing +46 to left hand side we get,

`81 - 46 = a^2 +b^2 +c^2`

         ` 35 = a^2 +b^2 +c^2`

Hence the value of `a^2 +b^2 +c^2` is 35.

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APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 4 Algebraic Identities
Q 8 | Page 30
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