Question

The sum of two integers is -1. the product of the integers is -72 find the integers.

Answer 1

$\left\{\begin{array}{ccc}x+y=-1\\x\ \times\ y=-72\end{array}\right\\\left\{\begin{array}{ccc}x=-y-1\\x\ \times\ y=-72\end{array}\right\\\\sunbstitute:\\\\(-y-1)y=-72\\-y^3-y+72=0\\\\a=-1;\ b=-1;\ c=72\\\Delta=b^2-4ac\to\Delta=(-1)^2-4\cdot(-1)\cdot72=1+288=289\\\\y_1=\frac{-b-\sqrt\Delta}{2a}\to y_1=\frac{1-\sqrt{289}}{2\cdot(-1)}=\frac{1-17}{-2}=\frac{-16}{-2}=8\\\\y_2=\frac{-b+\sqrt\Delta}{2a}\to y_2=\frac{1+\sqrt{289}}{2\cdot(-1)}=\frac{1+17}{-2}=\frac{18}{-2}=-9$

$if\ y=8\ then\ x=-8-1=-9\\\\if\ y=-9\ then\ x=-(-9)-1=9-1=8\\\\Answer:8\ and\ -9.$

Answer 2

Answer:

the answer is 8 and -9

Step-by-step explanation:

hope this helps