Question

One number is $7$ more than another and its square is $77$ more than the square of the smaller number. What are the numbers?

Answer 1

Solution:

Let $x=$ the smaller number.

Let $x+7=$ the larger number.

$(x+7{)}^2=x^2+77$

$x^2+14x+49=x^2+77$

$14x=28$

$x=2$

$x+7=9$