Let a, b, c be non-zero real numbers such tha | vedclass

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Question

(b)

Given, $a+b+c=0 \Rightarrow a, b, c \in R$

$\Rightarrow \quad a^2+b^2+c^2=q$

$\Rightarrow \quad a^4+b^4+c^4=r$

$\Rightarrow \quad\left

Vedclass · Accepted Answer

$q^2=2 r$ always

Vedclass · Answer

(b)

Given, $a+b+c=0 \Rightarrow a, b, c \in R$

$\Rightarrow \quad a^2+b^2+c^2=q$

$\Rightarrow \quad a^4+b^4+c^4=r$

$\Rightarrow \quad\left(a^2+b^2+c^2ight)^2=a^4+b^4+c^4 +2\left(a^2 b^2+b^2 c^2+c^2 a^2ight)$

$\left(a^2+b^2+c^2ight)^2=a^4+b^4+c^4+2 \left[(a b+b c+c a)^2-2 a b c(a+b+c)ight]$

$q^2=r+2\left[(a b+b c+c a)^2-2(a b c)(0)ight]$

$q^2=r+2[a b+b c+c a]^2$

$q^2=r+2  \left[\begin{array}{c}(a+b+c)^2-\left(a^2+b^2+c^2ight) \ 2\end{array}ight]^2$

$q^2=r+2\left(\frac{0-q}{2}ight)^2$

$q^2=r+\frac{2 q^2}{4}$

$q^2-\frac{1}{2} q^2=r$

$q^2=2 r$

Let $a, b, c$ be non-zero real numbers such that $a+b+c=0$, let $q=a^2+b^2+c^2$ and $r=a^4+b^4+c^4$. Then,

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