If a-b-c-9 - a n d - 2a b-b c-c a-46- -then - a - 2- b - 2- c - 2 isA- 32B- 58C- 53D- 35

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Byju's Answer

Standard VIII

Mathematics

Expansion of (a+b+c)^2

If a+b+c=9 ∼ ...

Question

If $a + b + c = 9 a n d 2 (a b + b c + c a) = 46, t h e n a^{2} + b^{2} + c^{2}$ is :

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Solution

The correct option is D 35
Given, $a + b + c = 9 a n d 2 (a b + b c + c a) = 46$ .
Using the identity $(a + b + c)^{2} = a^{2} + b^{2} + c^{2} + 2 a b + 2 b c + 2 c a$ ,
$\Rightarrow$ $9^{2} = a^{2} + b^{2} + c^{2} + 46$
$\Rightarrow$ $a^{2} + b^{2} + c^{2} = 9^{2} - 46 = 81 - 46 = 35$ .

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Similar questions

I f a + b + c = 10 a n d a^{2} + b^{2} + c^{2} = 38, t h e n (a b + b c + c a)

is :

Prove that $∣ ∣ ∣ ∣ ∣ \begin{matrix} b c - a^{2} & c a - b^{2} & a b - c^{2} c a - b^{2} & a b - c^{2} & b c - a^{2} a b - c^{2} & b c - a^{2} & c a - b^{2} \end{matrix} ∣ ∣ ∣ ∣ ∣$ is divisible by (a+b+c) and find the quotient.

Q. If

a + b + c = 9

and

a b + b c + c a = 26

, then the value of

a^{2} + b^{2} + c^{2} - 3

is _______.

Q. If

a + b + c = 9

and

a b + b c + c a = 15

, then find

a^{2} + b^{2} + c^{2}

Q. If

a^{2} + b^{2} + c^{2} = 35

and

a b + b c + c a = 23

; find

a + b + c

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If a+b+c=9 and 2(ab+bc+ca)=46, then a2+b2+c2 is :

The correct option is D 35Given, a+b+c=9 and 2(ab+bc+ca)=46. Using the identity ( a+b+c)2=a2+b2+c2+2ab+2bc+2ca, ⇒ 92=a2+b2+c2+46 ⇒ a2+b2+c2=92−46=81−46=35.

If $a + b + c = 9 a n d 2 (a b + b c + c a) = 46, t h e n a^{2} + b^{2} + c^{2}$ is :

The correct option is D 35
Given, $a + b + c = 9 a n d 2 (a b + b c + c a) = 46$ .
Using the identity $(a + b + c)^{2} = a^{2} + b^{2} + c^{2} + 2 a b + 2 b c + 2 c a$ ,
$\Rightarrow$ $9^{2} = a^{2} + b^{2} + c^{2} + 46$
$\Rightarrow$ $a^{2} + b^{2} + c^{2} = 9^{2} - 46 = 81 - 46 = 35$ .