Question

if x = 1 + √2 find the value of (x-1÷x)​

Answer 1

Answer:

Answer:

\left(x-\frac{1}{x}\right)^{3}=8

Step-by-step explanation:

Given \: x = 1-\sqrt{2}\:---(1)

\frac{1}{x}=\frac{1}{1-\sqrt{2}}\\=\frac{1+\sqrt{2}}{(1-\sqrt{2})(1+\sqrt{2})}

=\frac{1+\sqrt{2}}{1^{2}-(\sqrt{2})^{2}}\\=\frac{1+\sqrt{2}}{1-2}\\=-(1+\sqrt{2})\:--(2)

Now,\\\left(x-\frac{1}{x}\right)^{3}\\=\left(1-\sqrt{2}-[-(1+\sqrt{2})]\right)^{3}\\=\left(1-\sqrt{2}+1+\sqrt{2}\right)^{3}\\=2^{3}\\=8

Therefore,

\left(x-\frac{1}{x}\right)^{3}=8

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