# Two positive numbers have a difference of 8 and a product of 33. What are these numbers?

**Solution:**

Given, two positive numbers have a difference of 8 and a product of 33.

Le the first number be x

Second number be y

x - y = 8 -------------- (1)

x × y = 33 ------------ (2)

From (2), y = 33 / x

Substitute the value in (1)

x - 33/x = 8

x^{2} - 33 = 8x

x^{2} - 8x - 33 = 0

x^{2} - 11x + 3x - 33 = 0

x(x - 11) + 3(x - 11) = 0

(x + 3)(x - 11) = 0

x = -3 or 11

Since the given number is positive, x = 11

Put the value of x in (1)

11 - y = 8

y = 11 - 8

y = 3

**Verification:**

1) difference between numbers is 8

x - y = 8

LHS = 11 - 3

= 8

RHS = 8

LHS = RHS

2) product of two number is 33

x × y = 33

LHS = 11 × 3

= 33

RHS = 33

LHS = RHS

Hence proved.

Therefore, the two positive numbers are x = 11 and y = 3.

## Two positive numbers have a difference of 8 and a product of 33. What are these numbers?

**Summary:**

Two positive numbers have a difference of 8 and a product of 33. The numbers are 11 and 3.

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