Question

if a+1/a=6,then a4+1/a4 is equal to

Answer 1

Answer:

$value \: of \: a^{4}+\frac{1}{a^{4}}=1154$

Step-by-step explanation:

$Given \: a+\frac{1}{a}=6--(1)$

Squaring on both sides,we get

$\big(a+\frac{1}{a}\big)^{2}=6^{2}$

$\implies a^{2}+\frac{1}{a^{2}}+2\times a \times \frac{1}{a}=36$

$\implies a^{2}+\frac{1}{a^{2}}+2=36$

$\implies a^{2}+\frac{1}{a^{2}}=36-2$

$\implies a^{2}+\frac{1}{a^{2}}=34---(2)$

On Squaring equation (2) , we get

$\big(a^{2}+\frac{1}{a^{2}}\big)^{2}=(34)^{2}$

$\implies a^{4}+\frac{1}{a^{4}}+2\times a^{2} \times \frac{1}{a^{2}}=1156$

$\implies a^{4}+\frac{1}{a^{4}}+2=1156$

$\implies a^{4}+\frac{1}{a^{4}}=1156-2$

$\implies a^{4}+\frac{1}{a^{4}}=1154$

Therefore,

$value \: of \: a^{4}+\frac{1}{a^{4}}=1154$

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