Question

) If x = 2√3 + 2√2 evaluate : (x+1
/x)
2​

Answer 1

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

Hi we met again

As $x=2(\sqrt{3}+\sqrt{2} )$

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

We rationalize the denominator

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

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

$x+1/x=(2+1/2)*\sqrt{3} +(2-1/2)*\sqrt{2}$

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

As $x+1/x=\frac{1}{2}* (5\sqrt{3}+ 3\sqrt{2} )$

We square both sides

$(x+1/x)^2=(1/2)^2*(5\sqrt{3} +3\sqrt{2} )^2$

$(x+1/x)^2=(1/4)*(75+2*15\sqrt{6} +18)$

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