Question

Find two consecutive numbers whose squares have a sum of 85.

• A. 3 and 4
• B. 5 and 6
• C. 6 and 7
• D. 7 and 8

Answer 1

The correct option is C 6 and 7

Let the two numbers be x and (x + 1).
As per the question,
$x^2+(x+1{)}^2=85$
$\Rightarrow x^2+(x^2+2x+1)=85$
$\Rightarrow 2x^2+2x-84=0$
$\Rightarrow x^2+x-42=0$
$\Rightarrow x^2+7x-6x-42=0$
$\Rightarrow (x+7)(x-6)=0$
Thus, x = -7 or 6.
$\Rightarrow (x+1)=-6or7$.
Among the given options, 6 and 7 is the right answer.