Question

When the square of a number is increased by 24, the result is eleven times the original. Number find the number

Answer 1

the number can be either 8 or 3.

Explanation:

Let's define N as the "number"

We know that when the square of this number is increased by 24:

N^2 + 24

we got eleven times the original number, then:

N^2 + 24 = 11*N

We just need to solve this for N

To do it, we first move all the terms to one side of the equation:

N^2 - 11*N + 24 = 0

Now we can use the Bhaskara's formula for the zeros of a quadratic equation:

for a general quadratic equation:

a*x^2 + b*x + c = 0

the roots or zeros are given by:

`x = (-b \pm √(b^2 - 4*a*c) )/(2*a)`

We get then:

`N = (-(-11) \pm √((-11)^2 - 4*1*24) )/(2*1) = (11 \pm 5)/(2)`

So we have two solutions:

N = (11 + 5)/2 = 16/2 = 8

N = (11 - 5)/2 = 6/2 = 3

So the number can be either 8 or 3.