Question

If $a^2+b^2=41andab=4,$ find :

(i) (a - b)

(ii) (a + b)

Answer 1

(i) $(a-b{)}^2=a^2+b^2-2ab=41-2(4)=41-8=33\therefore a-b=\sqrt{33}$

(ii) $(a+b{)}^2=a^2+b^2+2ab=41+2(4)=41+8=49\Rightarrow (a+b{)}^2=49\therefore a+b=7$