Question

If x+1/x = 12, find the value of x^2+1/x^2​

Answer 1

$\boxed{\sf (a+b)^2=a^2+b^2+2ab}$

Now

$\\ \sf\longmapsto x+\dfrac{1}{x}=12$

$\\ \sf\longmapsto \left(x+\dfrac{1}{x}\right)^2=12^2$

$\\ \sf\longmapsto x^2+2\times x\times \dfrac{1}{x}+\left(\dfrac{1}{x}\right)^2=144$

$\\ \sf\longmapsto x^2+\dfrac{1}{x^2}+2=144$

$\\ \sf\longmapsto x^2+\dfrac{1}{x^2}=144-2=142$

Answer 2

Answer:

122

Step-by-step explanation:

x+1/x = 12

x + 1 = 12x

x = 1/11

（1/11）² + 1 / （1/11）² = 1/121 +1 /1/121 = 122