Question

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

Answer 1

Answer:

            8 and 9   or   -8 and -9

Step-by-step explanation:

x  -  first integer

x+1  - the next consecutive integer

x(x+1)  - their product

x(x + 1) - 147 = -75

x² + x - 72 = 0

$x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}=\dfrac{-1\pm\sqrt{1-4(-72)}}{2}=\dfrac{-1\pm\sqrt{289}}{2}\\\\\\x_1=\dfrac{-1+17}2=8\,,\qquad x_2\dfrac{-1-17}2=-9\\\\x_1+1=9\,,\qquad\qquad\qquad x_2+1=-8$