If x-1-x-2- find the value of x64-1-x64A- 0B- 1C- 4D- 2

The correct option is C 4 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 + ...

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Byju's Answer

Standard IX

Mathematics

Algebraic Identities

If x+1/x=2, f...

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
4

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

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 4 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

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