Question

State true or false.

The two numbers whose sum is 27 and product is 182 are 13 and 14.

• A. True
• B. False

Answer 1

The correct option is A

True

Assume that the numbers are $x$ and $27-x$.

Given that their product is 182.

$x(27-x)=182$

$27x-x^2=182$

$x^2+27x-182=0$

$x=\frac{27\pm \sqrt{729-728}}{2}$

$x=\frac{27\pm 1}{2}$

$x=14,13$

Putting $x$=14, we get $27-x$ = 13

Putting $x$=13, we get $27-x$ = 14

Therefore, the two numbers are 14 and 13.