Question

Find a pair of integers whose prodouct is-15 and whose difference is8.​

Answer 1

Let the two integers be m and n

Now according to the question,

mn= 15.....(1)

m-n= 8 ....(2)

From (2)

m=8+n

(8+n)*n= 15

8n + n^2 = 15

n^2 + 8n -15 = 0

On solving this quadratic equation

We get -3,-5

m-(-3)= 8

m+3=8

m= 5

mn = 15

5*n = 15

n= 3

Hence the two integers are 3,5

Hope it helps ｡◕‿◕｡

Answer 2

$\huge\tt{Question}$

• Find a pair of integers whose product is -15 and whose difference is 8.

$\huge\tt{Answer }$

$\sf{Let\: the \: integers\:=\:a,b}$

A.T.Q

$\bf{Difference\:=\:8}$

$\sf{a-b\:=\:8}$

$\sf{a\:=\:8+b}$

$\bf{Product\:=\:-15}$

$\sf{ab\:=\:-15 }$

$\sf{Put\:value \:of\:a }$

$\mapsto\sf{(8+b)(b)\:=\:-15}$

$\mapsto\sf{8b+\ b^{2}\:=\:-15 }$

$\mapsto\sf{\ b^{2}+8b+15\:=\:0}$

$\mapsto\sf{\ b^{2}+5b+3b+15\:=\:0}$

$\mapsto\sf{b(b+5)+3(b+5)\:=\:0}$

$\mapsto\sf{(b+5)(b+3)\:=\:0}$

$\sf\boxed{b\:= \:-5\:,\:-3}$

$\bf{a = 8-5 = 3}$

$\bf{a = 8-3 = 5}$

$\sf\boxed{a\: = \:3\: , \:5}$