Question

Find two consecutive natural numbers whose squares have the sum 85.

• A. -7 and -6
• B. 5 and 6
• C. 6 and 7
• D. both a and c

Answer 1

The correct option is C 6 and 7

Let the two consecutive numbers be $x$ and $x+1$
According to the question,
$x^2+(x+1{)}^2=85$
$\Rightarrow x^2+x^2+1+2x=85$
$\Rightarrow x^2+x-42=0$
$\Rightarrow x^2+7x-6x-42=0$
$\Rightarrow (x+7)(x-6)=0$
$\Rightarrow x=-7$ or $x=6$
But, the number should be natural numbers. So, x can't be negative.
Hence the consecutive numbers are 6 and 7.
So, option c is correct.