Answer:
larger = 11
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