Question

If $a^2+b^2=29andab=10$; find :

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

Answer 1

(i) $(a+b{)}^2=a^2+b^2+2ab\Rightarrow (a+b{)}^2=29+2\times 10\Rightarrow (a+b{)}^2=29+20\Rightarrow (a+b{)}^2=49\Rightarrow a+b=\sqrt{49}\Rightarrow a+b=7$.

(ii) $(a-b{)}^2=a^2+b^2-2ab\Rightarrow (a-b{)}^2=29-2\times 10\Rightarrow (a-b{)}^2=29-20\Rightarrow (a-b{)}^2=9\Rightarrow a-b=\sqrt{9}\Rightarrow a-b=3$.