Answer:
Given that,
One integer is 4 more than another.
Their product is 165.
Let the intergers be x and y.
Let x be the larger integer.
we get,
[tex]x=4+y----(1)[/tex][tex]xy=165----(2)[/tex]Substitute equation (1) in equation (2), we get,
[tex](4+y)y=165[/tex][tex]4y+y^2=165[/tex]Solving this we get,
[tex]y^2+4y-165=0[/tex]we get,
[tex]y^2+15y-11y-165=0[/tex][tex]y(y+15)-11(y+15)=0[/tex]Taking y+15 as common, we get
[tex](y+15)(y-11)=0[/tex][tex]y=-15\text{ or }y=11[/tex]Hence there are two possible solutions
when y=-15, we get x=-11,
And when y=11, we get x=15
Largest integer = -11 or 15
Smallest integer = -15 or 11
Answer is:
Largest integer = -11 or 15
Smallest integer = -15 or 11
