This question was uploaded on 04/01/22 on social media accounts.
Solution 1:
Given equations:
\[\color{red} {a+b=4}\]
\[\color{blue} {a^2+b^2=10}\]
We know that,
\[(\color{red} {a+b})^2=\color{blue} {a^2+b^2}+2\color{fuchsia} {ab}\]
\[\Rightarrow (\color{red} {4})^2=\color{blue} {10}+2\color{fuchsia} {ab}\]
\[\Rightarrow \color{fuchsia} {ab=3}\]
Now,
\[(\color{blue} {a^2+b^2})^2=a^4+b^4+2(\color{fuchsia} {ab})^2\]
\[\Rightarrow(\color{blue} {10})^2=a^4+b^4+2(\color{fuchsia} {3})^2\]
\[\Rightarrow a^4+b^4=82\]
