#### Question

Two number differ by 4 and their product is 192. Find the numbers?

#### Solution

Let two required numbers be *x *and (x + 4)

Then according to question

x(x + 4) = 192

x^{2} + 4x - 192 = 0

x^{2} + 16x - 12x - 192 = 0

x(x + 16) - 12(x + 16) = 0

(x + 16)(x - 12) = 0

x + 16 = 0

x = -16

Or

x - 12 = 0

x = 12

Since, *x *being a number,

Therefore,

When x = -16 then

x + 4 = -16 + 4 = -12

And when x = 12 then

x + 4 = 12 + 4 = 16

Thus, two consecutive number be either 12, 16 or -16, -12.

Is there an error in this question or solution?

#### APPEARS IN

Solution Two Number Differ by 4 and Their Product is 192. Find the Numbers? Concept: Solutions of Quadratic Equations by Factorization.