Question

$If \\ \\ a + a^{-1} = 2\sqrt{2}, \\ \\ then\ find\ the\ value\ of \\ \\ a^4 + a^{-4}$

Answer 1

here is your answer
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Answer 2

Answer:

34

Step-by-step explanation:

Here

$a + a^{-1}=2\sqrt 2$

or

$a + \frac{1}{a}=2\sqrt2$

Squaring both sides

$(a+\frac{1}{a})^2=(2\sqrt2)^2$

$a^2+\frac{1}{a^2}+2(a)(\frac{1}{a})=8$

$a^2+\frac{1}{a^2}+2=8$

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

Squaring both sides

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

$a^4+\frac{1}{a^4}+2(a^2)(\frac{1}{a^4})=36$

$a^4+\frac{1}{a^4}+2=36$

$a^4+\frac{1}{a^4}=34$

or

$a^4+a^{-4}=34$