Question

If x2+1/x2=6
Find the value of x4+1/x4

Answer 1

See this attached solution.

Hope it helps

Answer 2

Answer:

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

Explanation:

Given $x^{2}+\frac{1}{x^{2}}=6$-----(1)

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We know the algebraic identity:

a²+2ab+b²=(a+b)²

Or

a²+b² = (a+b)²-2ab

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Now,

$x^{4}+\frac{1}{x^{4}}$

= $\left(x^{2}+\frac{1}{x^{2}}\right)^{2}-2\cdot x\cdot \frac{1}{x}$

= $6^{2}-2$

=$36-2$

=$34$

Therefore,

$x^{4}+\frac{1}{x^{4}}$

= $34$

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