Question

If x = 2√3 + 2√2 , evaluate : x2
+
1/
x
2​

Answer 1

Answer:

hope it will help you:-)

Answer 2

Answer : $x^2+1/x^2=\frac{85+30\sqrt{6} }{4}$

If we find each value and add them

it will be so long that you can win a novel prize in New York

Instead we do it in the 'algebraic way'

If you square $x+1/x$

you will find that it becomes $x^2+2+1/x^2$

$(x+1/x)^2=x^2+2+1/x^2$

$(x+1/x)^2-2=x^2+1/x^2$, nice

Let's rationalize 1/x

$1/x=\frac{\sqrt{3} -\sqrt{2} }{2}$

Find the sum

$x+1/x=\frac{5}{2} \sqrt{3}+\frac{3}{2} \sqrt{2}$

Square both sides

$(x+1/x)^2=\frac{(5\sqrt{3} +3\sqrt{2} )^2}{4} =\frac{75+30\sqrt{6} +18}{4}$

We have

$(x+1/x)^2=\frac{93+30\sqrt{6}}{4}$

CONCLUSION

Now use what we've got

$(x+1/x)^2-2=\frac{93+30\sqrt{6}}{4}-\frac{8}{4} =\frac{85+30\sqrt{6} }{4}$