Question

Product of two consecutive natural numbers is 56. Find the smaller number.

• A. 7

Answer 1

The correct option is A 7
Let the smaller number be $x$, then the larger number will be $x+1$.

Given that their product is 56.

$\therefore x(x+1)=56x^2+x-56=0x^2+x+(\frac{1}{2}{)}^2–(\frac{1}{2}{)}^2-56=0x^2+(2\times \frac{1}{2})x+(\frac{1}{2}{)}^2–(\frac{1}{4}+56)=0(x+\frac{1}{2}{)}^2-\frac{225}{4}=0(x+\frac{1}{2}{)}^2=\frac{225}{4}x+\frac{1}{2}=\pm \frac{15}{2}x=\pm \frac{15}{2}-\frac{1}{2}$

$\Rightarrow x=\frac{15}{2}-\frac{1}{2},-\frac{15}{2}-\frac{1}{2}$

$\Rightarrow x=7,-8$

Since it is given that both are natural numbers, the value of x cannot be negative.

$\therefore$ The smaller number is 7.