Question

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

Answer 1

the answer is 8 and -9

Explanation:

hope this helps

Answer 2

`\left\{\begin{array}{ccc}x+y=-1\\x\ *\ y=-72\end{array}\right\\\left\{\begin{array}{ccc}x=-y-1\\x\ *\ 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=(-b-\sqrt\Delta)/(2a)\to y_1=(1-√(289))/(2\cdot(-1))=(1-17)/(-2)=(-16)/(-2)=8\\\\y_2=(-b+\sqrt\Delta)/(2a)\to y_2=(1+√(289))/(2\cdot(-1))=(1+17)/(-2)=(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.`