Question

If $a^2+b^2=10andab=3$; find :

(i) a -b (ii) a + b

Answer 1

(i) $(a-b{)}^2=a^2+b^2-2ab\Rightarrow (a-b{)}^2=10-2\times 3\Rightarrow (a-b{)}^2=10-6\Rightarrow (a-b{)}^2=4\Rightarrow (a-b)=\sqrt{4}\Rightarrow a-b=2$.

(ii) $(a+b{)}^2=a^2+b^2+2ab\Rightarrow (a+b{)}^2=10+2\times 3\Rightarrow (a+b{)}^2=10+6\Rightarrow (a+b{)}^2=16\Rightarrow (a+b)=\sqrt{16}\Rightarrow (a+b)=4$.