Question

×+1/×=3 find x^2+(1/x)^2​

Answer 1

Answer:

Given,

$x + \frac{1}{x} = 3$

Squaring both sides,, we get,

$:→ {(x + \frac{1}{x} })^{2} = {3}^{2}$

Using formula :(a+b)²= a²+b²+2ab

$:→( {x})^{2} + {( \frac{1}{x} })^{2} + 2 \times x \times \frac{1}{x} = 9$

$:→ {x}^{2} + \frac{1}{ {x}^{2} } + 2 = 9$

$:→ {x}^{2} + \frac{1}{ {x}^{2} } = 9 - 2$

$:→ {x}^{2} + \frac{1}{ {x}^{2} } =7$

Hence, the answer is 7.

Answer 2

$( {x + \frac{1}{x} })^{2} = {x}^{2} + ( { \frac{1}{x} })^{2} + 2 \times x \times \frac{1}{x} \\ {3 }^{2} = {x }^{2} + \frac{1}{ {x}^{2} } + 2 \\ {x }^{2} + \frac{1}{ {x}^{2} } = 9 - 2 = 7$