Question

If $a+b=5$ and $ab=6$, then find $a^2+b^2$.

Answer 1

Finding the required value:

Given: $a+b=5$, $ab=6$

We know that, ${\left(a+b\right)}^2=a^2+b^2+2ab$

Substituting the values.

$$\begin{gathered} \Rightarrow 5^2=a^2+b^2+2\left(6\right) \\ \Rightarrow 25=a^2+b^2+12 \\ \Rightarrow 25-12=a^2+b^2 \\ \Rightarrow a^2+b^2=13 \end{gathered}$$

Hence, the value of $a^2+b^2$ is $13$.