Question

If a - b = 2, ab = 3 find the value of a2+b2__?​

Answer 1

a=b+2

ab=3

(b+2)b=3

$b {}^{2} + 2b - 3 = 0 \\ b {}^{2} + 3b - b - 3 = 0 \\ b(b + 3) - 1(b + 3) = 0 \\ (b + 3)(b - 1) = 0$

b=-3,a=-1

b=1,a=3

$a {}^{2} + b {}^{2} \\ = 1 + 9 \\ = 10$

Answer 2

${(a - b)}^{2} = {a}^{2} + {b}^{2} - 2ab$

${2}^{2} = {a}^{2} + {b}^{2} - 2 \times 3$

$4 = {a}^{2} + {b}^{2} - 6$

${a}^{2} + {b}^{2} = 4 + 6$

${a}^{2} + {b}^{2} = 10$