Question

x+1/x+2=6 is given. Find (x+2)^2+1/(x+2)^2.

Answer 1

\[\frac{ x+1 }{ x+2 } = 6\]

Answer 2

that right?

Answer 3

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

Answer 4

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

Answer 5

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

Answer 6

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

Answer 7

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

Answer 8

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

Answer 9

ans square both sides

Answer 10

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

Answer 11

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