Question

. If p =3-√5/3+√5 and q=3+√5/3-√5,find the value of p²+q².​

Answer 1

To find:

$\left(\frac{3-\sqrt{5}}{3+\sqrt{5}}\right)^2+\left(\frac{3+\sqrt{5}}{3-\sqrt{5}}\right)^2$

Simplifying the expression...

$\frac{7-3\sqrt{5}}{7+3\sqrt{5}}+\frac{7+3\sqrt{5}}{7-3\sqrt{5}}$

Finding LCM of denominator,

$\frac{\left(7-3\sqrt{5}\right)^2+\left(7+3\sqrt{5}\right)^2}{\left(7+3\sqrt{5}\right)\left(7-3\sqrt{5}\right)}$

Simplifying the denominator,

$\frac{\left(7-3\sqrt{5}\right)^2+\left(7+3\sqrt{5}\right)^2}{4}$

Simplifying the numerator,

$\frac{188}{4}$

Dividing

$47$