Question

The product of two consecutive integers is 90.find the integers

Answer 1

Answer:

$\boxed{\boxed{\boxed{ \sf The \: Consecutive \:numbers\: can \:be\: (9,10) or (-10,-9)}}}$

Step-by-step explanation:

Let the two consecutive integers be x and (x+1)

Then according to the Question ,

x × (x+1) = 90

On Opening the bracket,

x² + x = 90

$\implies$ x²+x-90 = 0

On spliitting the middle term to solve the quatratic equation ,

x²+ 10x - 9x -90 = 0

x(x+10) - 9(x+10) = 0

(x+10) (x-9) = 0

Therefore,

x = -10

and

x = 9

$\bigstar$ If , x = -10

Then the numbers will be

x = -10

and

(-10+ 1) = -9

$\bigstar$ If , x = 9

Then the numbers will be

x = 9

and

(9+1) = 10

$\bigstar$ So the consecutive integers can be

9,10

or

-10,-9