If x - 1-x - 2- find the value of x64 - 1-x64

X +1/x = 2 Squaring both sides, we get x^2 + 1/x^2+ 2.x.1/x = 4 So, x^2 + 1/x^2 = 4 2 = 2 Again Squaring both sides, we get x^4 + 1/x^4+ 2.x^2.1/x^2 = 4 ⇒x^ ...

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Standard IX

Mathematics

Normal Form to Standard Form

If x + 1/x = ...

Question

$If x + \frac{1}{x} = 2, find the value of x^{64} + \frac{1}{x^{64}}$

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Solution

The correct option is D
2

$x + \frac{1}{x} = 2$

Squaring both sides, we get $x^{2} + \frac{1}{x^{2}} + 2. x . \frac{1}{x} = 4$
So, $x^{2} + \frac{1}{x^{2}} = 4 - 2 = 2$
Again Squaring both sides, we get $x^{4} + \frac{1}{x^{4}} + 2. x^{2} . \frac{1}{x^{2}} = 4$
$\Rightarrow x^{4} + \frac{1}{x^{4}} = 4 - 2 = 2$

Similarly, $x^{8} + \frac{1}{x^{8}} = x^{32} + \frac{1}{x^{32}} = x^{64} + \frac{1}{x^{64}} = 2$

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If x+1x=2, find the value of x64+1x64

The correct option is D 2 x+1x=2 Squaring both sides, we get x2+1x2+2.x.1x=4 So, x2+1x2=4−2=2 Again Squaring both sides, we get x4+1x4+2.x2.1x2=4 ⇒x4+1x4=4−2=2 Similarly, x8+1x8=x32+1x32=x64+1x64=2

$If x + \frac{1}{x} = 2, find the value of x^{64} + \frac{1}{x^{64}}$