Question

Tick (✓) the correct answer:
If (a − b) = 7 and ab = 9, then (a² + b²) = ?
(a) 67
(b) 31
(c) 40
(d) 58

Answer 1

(a) 67

$$\begin{gathered} \left(a-b\right)=7 \\ \Rightarrow \mathrm{Squaring}\mathrm{both}\mathrm{the}\mathrm{sides}: \\ \Rightarrow {\left(a-b\right)}^2={\left(7\right)}^2 \\ \Rightarrow \left(a^2+b^2-2ab\right)=49 \\ \Rightarrow \left(a^2+b^2\right)=49+2ab \\ \Rightarrow \left(a^2+b^2\right)=49+2\left(9\right) \\ \Rightarrow \left(a^2+b^2\right)=49+18 \\ \Rightarrow \left(a^2+b^2\right)=67 \end{gathered}$$