Question

Find a pair of integers whose product is-36 and whose diffence is 15.​

Answer 1

Answer: $(12,-3)\ \text{or}\ (3,-12)$

Step-by-step explanation:

Given

The product of integers is -36

The difference of integers is 15

Suppose the integers are x and y

$\Rightarrow x-y=15\\\Rightarrow x=15+y\\\Rightarrow xy=-36$

Put the value of $x$ in the product

$\Rightarrow (15+y)y=-36\\\Rightarrow 15y+y^2+36=0\\\Rightarrow y^2+12y+3y+36=0\\\Rightarrow y(y+12)+3(y+12)=0\\\Rightarrow (y+12)(y+3)=0\\\Rightarrow y=-3\ \text{or}\ -12$

$\therefore x=12\ \text{or}\ 3$

Pairs of integers are $(12,-3)\ \text{or}\ (3,-12)$