Question

if ( x + 1/x)² = 3, then x⁶ = ?
please it's urgent. Don't write unnecessary answer if someone give me correct answer I will follow him and thank him.​

Answer 1

Step-by-step explanation:

$(x+\frac{1}{x} )^{2} =3$

$x+\frac{1}{x} =\sqrt{3}$

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

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

Now substitute the value of $x+\frac{1}{x}$ as √3 in the equation.

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

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

$x^{3} +\frac{1}{x^{3} } =0$

$(x^{3} +\frac{1}{x^{3} } )^{2} =(0)^{2}$

$(x^{6} +2+\frac{1}{x^{6} }) =0$

$x^{6} +\frac{1}{x^{6} } =0-2$

$x^{6} +\frac{1}{x^{6} } =-2$

∴$x^{6}=-2-\frac{1}{x^{6} }$

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