Question

if x=3-2√2, find the value of x^3-1/x^3
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Answer 1

Answer:

-140√2

Step-by-step explanation:

x=3-2√2

so,

$\frac{1}{x}=\frac{1}{3-2\sqrt2} = \frac{3+2\sqrt2}{(3-2\sqrt2)(3+2\sqrt2)}=\frac{3+2\sqrt2}{3^2-(2\sqrt2)^2}=\frac{3+2\sqrt2}{9-8}=\frac{3+2\sqrt2}{1}=3+2\sqrt2$

Now,$x-\frac{1}{x} = -4\sqrt2$

$x^3-\frac{1}{x^3} =(x-\frac{1}{x})^3+3x\frac{1}{x}(x-\frac{1}{x}) =(x-\frac{1}{x})^3+3(x-\frac{1}{x})$

=(-4√2)³+3(-4√2)

= -128√2 -12√2

= -140√2