Question

if a= (1/2+√3) b= (1/2-√3). Then solve it, (1/a^2 + 1) + (1/b^2 + 1)​

Answer 1

Rationalize the denominator.

$a=2-\sqrt{3}$ & $b=2+\sqrt{3}$

Then

$a+b=4$ & $ab=1$

→ $a^2+b^2=14$

Expand IN ORDER TO use the value above

$(\frac{1}{a^2} +1)(\frac{1}{b^2}+1)$

→ $\frac{1}{a^2b^2} +\frac{1}{a^2} +\frac{1}{b^2} +1$

TAKING L.C.M

$\frac{a^2b^2+a^2+b^2+1}{a^2b^2}$

→ $1^2+14+1=16$

THE ANSWER IS 16