Question

If the sum of squares of two consecutive numbers is $41$, then the numbers are ____.

• A. $(5,6)$
• B. $(4,5)$
• C. $(6,7)$
• D. $(4,3)$

Answer 1

Answer: (B)

$(4,5)$

Let the numbers be x and x+1

$\Rightarrow x^2+(x+1{)}^2=41$

$\Rightarrow x^2+x-20=0$

$\Rightarrow (x+5)(x-4)=0$

$\Rightarrow x=4$ and $x\ne -5$ as number can't be negative

$\therefore$numbers are x and $x+1=4$ and $5$