2(x+1/x)2=10-x-1/x

Solution for 2(x+1/x)2=10-x-1/x equation:

2(x+1/x)2=10-x-1/x

We move all terms to the left:

2(x+1/x)2-(10-x-1/x)=0


Domain of the equation: x)2!=0

x!=0/1

x!=0

x∈R



Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

2(+x+1/x)2-(-1x-1/x+10)=0

We multiply parentheses

4x+4x-(-1x-1/x+10)=0

We get rid of parentheses

4x+4x+1x+1/x-10=0

We multiply all the terms by the denominator


4x*x+4x*x+1x*x-10*x+1=0

We add all the numbers together, and all the variables

-10x+4x*x+4x*x+1x*x+1=0

Wy multiply elements

4x^2+4x^2+x^2-10x+1=0

We add all the numbers together, and all the variables

9x^2-10x+1=0

a = 9; b = -10; c = +1;
Δ = b2-4ac
Δ = -102-4·9·1
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-8}{2*9}=\frac{2}{18}
=1/9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+8}{2*9}=\frac{18}{18}
=1
$