Question

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

• 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 will be $x$+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

$(x+\frac{1}{2})$ = $\pm$ $\frac{15}{2}$,

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

$x$ = 7, -8

The required number is 7