Question

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 larger number?

Answer 1

Explanation:

x - y = 7...eqn 1

x^2 + y = 125...eqn 2

making y the subject of the formula in eqn 1

=> y = x -7...eqn 3

subst for y from eqn 3 in eqn 2

=> x^2 + x-7 = 125

=> x^2 + x - 132 = 0

=> (x + 12) (x -11) =0

x = 11 or -12

when x = 11, y = 4

when x = -12, y = -19

Answer 2

The largest numbers is either -12 or 11

Explanation:

Let the numbers be a and b and a be the largest number.

The difference of two numbers is 7

a - b = 7 ------------------------- eqn 1

The sum of the smaller number and the square of the larger number is 125

a² + b = 125 ------------------------- eqn 2

eqn 1 + eqn 2

a² + a - 132 = 0

( a + 12 ) (a - 11) = 0

a = -12 or a = 11

So the largest numbers is either -12 or 11