## anonymous one year ago x+1/x+2=6 is given. Find (x+2)^2+1/(x+2)^2.

1. DanJS

$\frac{ x+1 }{ x+2 } = 6$

2. DanJS

that right?

3. DanJS

(x+1)/(x+2) = 6

4. anonymous

$x+\frac{ 1 }{x+2 }=6, (x+2)^2+\frac{ 1 }{ (x+2)^{2}}=?$

5. DanJS

solve the equation for x, then use that x in the expression to find a value

6. mathmath333

\large \color{black}{\begin{align} & x+2+\frac{ 1 }{x+2 }=8, \hspace{.33em}\\~\\ \end{align}}

7. mathmath333

\large \color{black}{\begin{align} & put\ \ x+2=a \hspace{.33em}\\~\\ \end{align}}

8. anonymous

ok thank you i could not think i should add 2 to both sides so the answer is 62

9. mathmath333

ans square both sides

10. ganeshie8

that is clever! $$a+\frac{1}{a} = k \implies a^2+\frac{1}{a^2} = k^2-2$$

11. DanJS

yeah, looks like that was the point of the problem.. nice