Question

What are two consecutive integers that their product, minus 147, is equal to -75?

Answer 1

8 and 9 or -8 and -9

Explanation:

x - first integer

x+1 - the next consecutive integer

x(x+1) - their product

x(x + 1) - 147 = -75

x² + x - 72 = 0

`x=(-b\pm√(b^2-4ac))/(2a)=(-1\pm√(1-4(-72)))/(2)=(-1\pm√(289))/(2)\\\\\\x_1=\frac{-1+17}2=8\,,\qquad x_2\frac{-1-17}2=-9\\\\x_1+1=9\,,\qquad\qquad\qquad x_2+1=-8`