Question

The difference between the squares of two consecutive even numbers is 92.Find the sum of their squares.

• A. 1252
• B. 340
• C. 1460
• D. 1060

Answer 1

The correct option is D 1060

let n,n+2 be two consective even numbers

Given $(n+2{)}^2-n^2=92$

$\Rightarrow (n+2n)(n+2+n)=92$ $[\because a^2-b^2=(a-b(a+b)]$

$\Rightarrow 2(2n+2)=92$

$\Rightarrow 2n+2=\frac{92}{2}$

$\Rightarrow 2n=46-2$

$\Rightarrow n=\frac{44}{2}$

$\Rightarrow n=22.$

$\therefore (n+2{)}^2+n^2=(22+2{)}^2+(22{)}^2$

$=(24{)}^2+(22{)}^2$

=576+484

1060.