Question

If x+1/x=6, find the value of x²+1/x²​

Answer 1

Step-by-step explanation:

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Answer 2

Step-by-step explanation:

Given : The value of $x+\frac{1}{x}=6$.

To find : The value of $x^{2} +\frac{1}{x^{2} }$

Formula used : We use an algebraic identity,

$(a+b)^{2} =a^{2} +b^{2} +2ab$

• Calculation for $x^{2} +\frac{1}{x^{2} }$

we have

$x+\frac{1}{x}=6$

for finding the value of $x^{2} +\frac{1}{x^{2} }$  we can start with the algebraic identity in which we take,

$a=x$   and $b=\frac{1}{x}$ ,

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

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

$x^{2} +\frac{1}{x^{2} }+2 =36$

$x^{2} +\frac{1}{x^{2} } =36-2$

$x^{2} +\frac{1}{x^{2} }=34$

Hence, we get the value of $x^{2} +\frac{1}{x^{2} }=34$.