What is the sum of the squares of the following numbers ? √3 /(√2+1), √3/(√2-1), √2/√3

Question

What is the sum of the squares of the following numbers ?

\(\frac{\sqrt3}{\sqrt2+1} ,\frac{\sqrt3}{\sqrt2-1}, \frac{\sqrt2}{\sqrt3}\)

(a) 16

(b) 18

(c) 16\(\frac23\)

(d) 18\(\frac23\)

Answer 1

(d)  18\(\frac23\)

Required sum

= \(\frac{54+2}{3} = \frac{56}{3} = 18\frac23\)