Question

if a^2+ab=21, b^2+ab=-9, than find a-b​

Answer 1

(a-b) = 12/√30

Add first two equations

a² + b² + ab + ab = 9 + 21

a² + b² + 2ab = 30

(a+b)² = 30 — [ Formula]

a+b = √30 — [ By taking square roots]

Now , Substract two equations

(a² + ab)-(b²+ab) =21 - 9

a² - b² = 12

(a+b)(a-b) = 12 —[Formula]

√30 (a-b) = 12

a-b = 12/√30