Question

lf a+b= 9 and ab= -22, find a-b

Answer 1

${(a + b)}^{2} - {(a - b)}^{2} = 4ab \\ {(a - b)}^{2} = {9}^{2} - 4 \times - 22 = 169 \\ therefore \: \: a - b = \sqrt{169} \\ = 13 \: \: or \: \: - 13$

Answer 2

a+b=9
ab=-22
(a+b)^2=a^2+b^2+2ab
9^2=a^2+b^2-2×22
81=a^2+b^2-44
a^2+b^2=81+44=125
(a-b)^2=a^2+b^2-2ab
(a-b)^2=125-(2×-22)
(a-b)^2=125+44=169
a-b=√169=13