Question

16. If x = 4 + √15 and xy
= 1, then find
the value of x2+
y2​

Answer 1

Answer:

$y = \frac{1}{x} = \frac{1}{4 + \sqrt{15} } = \frac{1}{4 + \sqrt{15} } \times \frac{4 - \sqrt{15} }{4 - \sqrt{15} } = 4 - \sqrt{15}$

now,

${x}^{2} + {y}^{2} = (4 + \sqrt{15} ) {}^{2} + (4 - \sqrt{15} ) {}^{2} = 2(16 + 15) = 62$

Ans