Question

if x = 3-√13/2 find x^2 +1/x^2​

Answer 1

Answer:

-2

Step-by-step explanation:

(3-root13/2)^2+1/(3-root13/2)^2

9-13/4+1/9-13/4

9-13/4+1*4/9-13

9-13/4+4/9-13

-4/4+-4/4

-1+(-1)

-1-1

-2

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Answer 2

The correct answer is 11.

Given: $x=\frac{3-\sqrt{13} }{2}$.

To Find: The value of $x^{2} +\frac{1}{x^{2}}$.

Solution:

$x^{2} +\frac{1}{x^{2}}$

= $(x+\frac{1}{x} )^{2} -2x*\frac{1}{x}$

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

Now, $x=\frac{3-\sqrt{13} }{2}$

$(x+\frac{1}{x} )=(\frac{3-\sqrt{13} }{2}+\frac{2 }{3-\sqrt{13} } )$

Take LCM and add the terms.

= $\frac{(3-\sqrt{13})^{2} +4 }{2(3-\sqrt{13} )}$

= $\frac{9+13-6\sqrt{13}+4 }{6-2\sqrt{13} }$

= $\frac{26-6\sqrt{13} }{6-2\sqrt{13} }$

= $\frac{13-3\sqrt{13} }{3-\sqrt{13} }$

= $\frac{-\sqrt{13}( 3-\sqrt{13} ) }{3-\sqrt{13} }$

$x+\frac{1}{x}$ = $-\sqrt{13}$

$(x+\frac{1}{x} )^{2} -2$ = $(-\sqrt{13} )^{2} -2$

= 13 - 2

= 11

Hence, the answer is 11.

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