Question

The product of a number and 8 less than the number is 65 what are the numbers

Answer 1

let one no. be x. other no will be (x-8) as given in question : x*(x-8) =65 x*x-8x=65 x*x-8x-65=0 x*x-13x+5x-13*5=0 (x-13)(x-5)=0 x=13 &other no. x-8=13-8=5 ans. 13 and 5

Answer 2

Given: The product of a number and 8 less than the number is 65.

To find: We have to find out the numbers.

Solution:

Let one number be x.

Given that the other number is 8 are less than the number.

So, the second number is x-8.

The product of the two numbers is 65.

So, we can write-

$x(x - 8) = 65 \\ {x}^{2} - 8x - 65 = 0 \\ {x}^{2} - 13x + 5x - 65 = 0 \\ x(x - 13) + 5(x - 13) = 0 \\ (x - 13)(x + 5) = 0 \\ x = 13 \\ x = - 5$

So, the value of x is 13 or -5.

For 13 the value of the other number is 13-8=5.

For -5 the value of the other number is -5-8=-13.

Thus, the numbers are 13,5 or -5,-13.