The difference of two numbers is 7. If the sum of the smaller number and the square of the larger number is 125, what is the value of the larger number?

larger = 11

Step-by-step explanation:

We will consider x = bigger, y = smaller

This means x - y = 7 (The difference of two numbers is 7)

This also means that x = 7 + y

And

y + x^2 = 125 (The sum of the smaller number and the square of the larger number is 125)

If we sustitute x = 7 + y in the second equation we get

y + (7+y) ^2 = 125

We can do the square of the binomial and get

y + 49 + 14y + y^2 = 125 (We substract 125 on both sides of the equation)

y + 49 + 14y + y^2 - 125 = 125 - 125

We get

y^2 + 15y - 76 = 0

We can make a factorization

(y+19) (y-4) = 0

y+19 = 0 y-4 = 0

y = - 19 y=4

This means y=4 is the smaller number and x = 7 + y = 7 + 4 = 11

So x = 11 is the bigger number