Question

The product of two negative integers is 112. If one of the integer is 9 more than other than the greater integer is_______ -16,16,7,-7

Answer 1

Hey
here's your answer !!

Let the smaller number be x
There fore ,
The greater number will be ( x + 9 )

Acc. to the question ,
x ( x + 9 ) = 112 ,
=> x² + 9x - 112 = 0 ,
=> x² + 16x - 7x - 112 = 0 ,
=> x ( x + 16 ) - 7 ( x + 16 ) = 0 ,
=> ( x - 7 ) ( x + 16 ) = 0 .

So ,
either ( x - 7 ) = 0 or ( x + 16 ) = 0 .

so if ( x - 7 ) = 0 ,
then ( x + 16) = 0
=> x = -16 .

and if ( x + 16 ) = 0 ,
then ( x - 7 ) = 0
=> x = 7 .

But acc. to the question ,
x is a negative integer .
so, actual value of x is -16 .

so the two numbers are ----->
( a ) -16 .
( b ) -16 + 9 = -7 .

Hope it helps !!