Question

The difference between two positive numbers is 6.and their product is 216 what are the number

Answer 1

Step-by-step explanation:

how x and x+6 get................

Answer 2

The numbers are 12 and 18.

Given - Difference and product

Find - Numbers

Solution - Let the numbers be x and y.

As per first statement -

$x - y = 6$

As per second statement -

$x \times y = 216$

$x = \frac{216}{y}$

Keep the value of x in first equation.

$\frac{216}{y} - y = 6$

Multiplying this equation by y.

$- {y}^{2} + 216 = 6y$

Shifting 16y to LHS

${y}^{2} + 6y - 216 = 0$

${y}^{2} - 12y + 18y - 216 = 0$

$y(y - 12) + 18(y - 12) = 0$

$(y - 12)(y + 18) = 0$

$y = 12 \: and -18$

Since the numbers are positive, so, y = 12.

x = 6 + 12

x = 18

Hence, the numbers are 12 and 18.

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