Question

The product of 2 consecutive natural numbers is 56. Solve this problem using completing the square method of quadratic equation. Write the equation obtained after completing the square and also write the smaller of the 2 consecutive positive integers.

• A. 7, (x+1/2)² – 225/4 = 0
• B. 8, (x+1/2)² – 225/4 = 0
• C. 7, (x-1/2)² – 225/4 = 0
• D. 8, (x-1/2)² – 225/4 = 0

Answer 1

The correct option is A

7, (x+1/2)² – 225/4 = 0

Let the smaller number be $x$. The larger one is $x+1$.

Their product is $x(x+1)$.

$x(x+1)=56$

$x^2+x-56=0$

$x^2+x+(\frac{1}{2}{)}^2–(\frac{1}{2}{)}^2-56=0$

$(x+\frac{1}{2}{)}^2-\frac{225}{4}=0$

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

$x=7,-8$

The required number is 7.