Question

If x =4-root 15 find the value of x^2 + 1/x^2

Answer 1

x = 4 - √15
x² = 16 + 15 - 8√15 = 31 - 8√15
1/x² = 1/31 - 8√15 = (31+8√15) / 961-960 = 31+8√15

x² + 1/x² = 62

Answer 2

Answer:

62

Step-by-step explanation:

Given,

$x=4-\sqrt{15}$

$\implies \frac{1}{x}=\frac{1}{4-\sqrt{15}}$

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

$=\frac{4+\sqrt{15}}{(4)^2-(\sqrt{15})^2}$

$=\frac{4+\sqrt{15}}{16-15}$

$=\frac{4+\sqrt{15}}{1}$

$=4+\sqrt{15}$

Thus,

$x^2+\frac{1}{x^2}=(4-\sqrt{15})^2+(4+\sqrt{15})^2$

$=16+15-20\sqrt{15}+16+15+20\sqrt{15}$

( Because, (a±b)² = a² ± 2ab + b² )

$=62$