Question

ifa+1/a=
root 2, then find a (power) 4 +1/a (power) 4.. I need help please do it fast it's a request

Answer 1

$Given \:a + \frac{1}{a} = \sqrt{2} \: ---(1)$

$We \:know \: that ,\\a^{2} + \frac{1}{a^{2}} = \Big(a +\frac{1}{a}\Big)^{2} - 2 \\= (\sqrt{2})^{2} - 2 \: [From \:(1) ]$

$= 2 - 2 \\= 0 \:--(2)$

$Now ,a^{4} + \frac{1}{a^{4} }= \Big(a^{2} +\frac{1}{a^{2}}\Big)^{2} - 2 \\= 0 - 2 \\= -2 \: --(3)$

Therefore.,

$\red{a^{2} + \frac{1}{a^{2}}}\green { = 0}$

$\red{ a^{4} + \frac{1}{a^{4}}} \green {= -2 }$

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