Question

(a-1/a)² = 3 then (a^6+1/a^6)=?​

Answer 1

Answer:

Step-by-step explanation:

Answer 2

The required solution is 110

Step-by-step explanation:

It is given that:

$(a-\frac{1}{a})^{2} =3$

We have to find $a^{6} +\frac{1}{a^{6}}$

We will first solve the given equation using:$(a-b)^{2} =a^{2} +b^{2} -2ab$

$(a-\frac{1}{a})^{2} =3\\\\\Rightarrow a^{2} +(\frac{1}{a} )^{2} -2\times a\times \frac{1}{a} =3\\\\\Rightarrow a^{2} +\frac{1}{a^{2} } -2=3\\\\\Rightarrow a^{2} +\frac{1}{a^{2} } =3+2\\\\\Rightarrow a^{2} +\frac{1}{a^{2} }=5$

Now take whole cube on both sides

$\Rightarrow (a^{2} +\frac{1}{a^{2} })^{3} =(5)^{3}$

We will use $(a+b)^{3}=a^{3}+b^{3}+3ab(a+b)$

$\Rightarrow (a^{2})^{3}+(\frac{1}{a^{2} } )^{3}+3\times a^{2}\times\frac{1}{a^{2} }(a^{2}+\frac{1}{a^{2} })=125$

Substituting $(a^{2}+\frac{1}{a^{2} })=5$

$\Rightarrow (a^{2})^{3}+(\frac{1}{a^{2} } )^{3}+3(5)=125\\\\\Rightarrow a^{6}+\frac{1}{a^{6}}+15=125\\\\\Rightarrow a^{6}+\frac{1}{a^{6}}=125-15\\\\\Rightarrow a^{6}+\frac{1}{a^{6}}=110$

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If x+1/x=3 then x^6+1/x^6=

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