Question

If x=4−√15, find the value of x^2+1/x^2

Answer 1

Answer:

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

Step-by-step explanation:

Answer 2

Answer:

$x = 4 - \sqrt{15} \\ \\ \frac{1}{x} = 4 + \sqrt{5}$

${x}^{2} = {4}^{2} + { \sqrt{5} }^{2} - 8 \sqrt{5} \\ \\ = 21 - 8 \sqrt{5}$

$\frac{1}{ {x}^{2} } = 21 + 8 \sqrt{5}$

NOW X^2 +1/X^2:

$21 + 8 \sqrt{5} + 21 - 8 \sqrt{5} \\ \\ = 42$