Question

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

Answer 1

122

Explanation:

x+1/x = 12

x + 1 = 12x

x = 1/11

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

Answer 2

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

Now

`\\ \sf\longmapsto x+(1)/(x)=12`

`\\ \sf\longmapsto \left(x+(1)/(x)\right)^2=12^2`

`\\ \sf\longmapsto x^2+2* x* (1)/(x)+\left((1)/(x)\right)^2=144`

`\\ \sf\longmapsto x^2+(1)/(x^2)+2=144`

`\\ \sf\longmapsto x^2+(1)/(x^2)=144-2=142`