Question

Tick (✓) the correct answer:
If (a + b) = 12 and ab = 14, then (a² + b²) = ?
(a) 172
(b) 116
(c) 165
(d) 126

Answer 1

(b) 116

$$\begin{gathered} \left(a+b\right)=12 \\ \Rightarrow Squaringboththesides: \\ \Rightarrow {\left(a+b\right)}^2={\left(12\right)}^2 \\ \Rightarrow \left(a^2+b^2+2ab\right)=144 \\ \Rightarrow \left(a^2+b^2\right)=144-2ab \\ \Rightarrow \left(a^2+b^2\right)=144-2\left(14\right) \\ \Rightarrow \left(a^2+b^2\right)=144-28 \\ \Rightarrow \left(a^2+b^2\right)=116 \end{gathered}$$