Question

If a + b + c = 0,

a ^2 + b^2+ c^2= 10
, then the value of

a^4+ b^4+ c^4 is ...​

Answer 1

$\huge✎\fbox \orange{QUE} ST \fbox\green{ION}☟$

$If \:a + b + c = 0,$

$a ^2 + b^2+ c^2= 1,$

$Then \:the\: value \:of$

$a^4+ b^4+ c^4 \:is$

$\huge✍︎\fbox\orange{ÂŇ}\fbox{SW} \fbox\green{ÊŘ}:$

Given:

${\: a+b+c=0 \: and \: a²+b²+c²=1}$

${a+b+c=0}$

Squaring on both sides,

${a²+b²+c²+2(ab+bc+ca)=0}$

$⇒ab+bc+ca= \frac{1}{2}$

Squaring on both sides,

$a²b²+b²c²+c²a²+2abc(a+b+c) = \frac{1}{4}$

${⇒a²b²+b²c²+c²a² = \frac{1}{4} }$

${Now,a⁴+b⁴+c⁴}{= (a²+b²+c²)²}$

$-{2(a²b²+b²c²+c²+a²)}$

$\therefore \: {a}^{4} + {b}^{4} + {c}^{4}$

$= 1 - 2\frac{1}{4} = \frac{1}{2}$

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