Question

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

• A. 9
• B. 8
• C. 7
• D. 6

Answer 1

The correct option is C 7

Let the smaller number be $x$.
Then the larger one will be $x+1$.
Their product is $x(x+1)$.
Given, their product is 56.
$x(x+1)=56x^2+x-56=0x^2+x=56$

Adding the square of one-half of the coefficient of x [i.e., $(\frac{1}{2}{)}^2$] to both sides, we get,

$x^2+x+(\frac{1}{2}{)}^2=(\frac{1}{2}{)}^2+56(x{)}^2+2\times x\times \frac{1}{2}+(\frac{1}{2}{)}^2=\frac{1}{4}+56(x+\frac{1}{2}{)}^2=\frac{225}{4}x+\frac{1}{2}=\pm \frac{15}{2}⟹x=\frac{15}{2}-\frac{1}{2},x=-\frac{15}{2}-\frac{1}{2}\therefore x=7,-8$

As the given numbers are natural numbers, the smaller number is 7.