Question

Two numbers if we multiply we get - 1500 and if we add we get - 40

Answer 1

Let the numbers be x and y.

x+y = -40........(1)

xy = -1500

y = -1500/x

(1) becomes

x - (1500/x) = -40

x^2 - 1500 = -40x

x^2 +40x - 1500 = 0

Now I solve this equation by square completion method.

x^2 + 40x = 1500

x^2 + 40x +400 = 1500 + 400

( x+ 20)^2 = 1900

x+20 =10 sqrt(19)
(or) x+20 = -10 sqrt(19)

x=-20+10 sqrt(19)
(or) x=-20 -10 sqrt(19)

I hope this answer helps you