Question

Q.if X+1/X=9, find the value of X4+1/X4?

Answer 1

Answer:

$x^{4}+\frac{1}{x^{4}}=6239$

Step-by-step explanation:

$Given\:x+\frac{1}{x}=9\:---(1)$

/* On Squaring both sides, we get

$\left(x+\frac{1}{x}\right)^{2}=9^{2}$

$\implies x^{2}+\frac{1}{x^{2}}+2\times x\times \frac{1}{x}=81$

$\implies x^{2}+\frac{1}{x^{2}}+2=81$

$\implies x^{2}+\frac{1}{x^{2}}=81-2$

$\implies x^{2}+\frac{1}{x^{2}}=79\:--(2)$

/* On Squaring equation (2), we get

$x^{4}+\frac{1}{x^{4}}+2=79^{2}$

$x^{4}+\frac{1}{x^{4}}+2=6241$

$x^{4}+\frac{1}{x^{4}}=6241-2\\=6239$

Therefore,

$x^{4}+\frac{1}{x^{4}}=6239$

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