Question

How to solve 1=(4s+5)^1/2-(2s+2)^1/2 please show steps.

Answer 1

\(\bf \large 1=(4s+5)^{\frac{1}{2}}-(2s+2)^{\frac{1}{2}}\implies 1=\sqrt{4s+5}-\sqrt{2s+2}
\\ \quad \\
1+\sqrt{2s+2}=\sqrt{4s+5}\qquad \textit{squaring both sides}
\\ \quad \\
1^2+2\sqrt{2s+2}+2s+2=4s+5\implies 3+2s+2\sqrt{2s+2}=4s+5
\\ \quad \\
2\sqrt{2s+2}=2s+2\qquad \qquad {\color{blue}{ u=\sqrt{2s+2}}}
\\ \quad \\
2{\color{blue}{ u}}={\color{blue}{ u}}^2\implies 0={\color{blue}{ u}}^2-2{\color{blue}{ u}}\)

and I think you can take it from there