Question

If x = 3-2√2 , find x^2+1/x^2​

Answer 1

Answer:

34

Step-by-step

x=3-2√2

x^2+1/x^2

=(3-2√2)^2+1/（3-2√2)^2

=9+8-12√2+1/9+8-12√2

=17-12√2+1/(17-12√2)

=17-12√2+(17+12√2)/(17-12√2)(17+12√2)

=17-12√2+(17+12√2)/17^2-(12√2)^2

=17-12√2+(17+12√2)/289-288

=17-12√2+17+12√2

=17+17

=34

Answer 2

Step-by-step explanation:

$x = 3 - 2 \sqrt{2} \\ {x}^{2} + \frac{1}{ {x}^{2} } \\ = {x}^{2} + \frac{ 1}{ {x}^{2} } + 2 \times \frac{1}{x} \times \frac{1}{x} - 2 \times \frac{1}{x} \times \frac{1}{x} \\ = ( {x + \frac{1} {x} )}^{2} - 2 \\ = ( {3 - 2 \sqrt{2} + \frac{1}{3 - 2 \sqrt{2} } ) }^{2} - 2 \\ = ( { {3}^{2} - {(2 \sqrt{2}) }^{2} + 1)}^{2} \times \frac{1}{ {(3 - 2 \sqrt{2}) }^{2} } - 2 \\ = {(9 - 12 \sqrt{2} + 8 + 1) }^{2} \times \frac{1}{9 - 12 \sqrt{2} + 8} - 2 \\ = ({18 - 12 \sqrt{2} )}^{2} \times \frac{1}{17 - 12 \sqrt{2} } - 2$