Question

one number is 7 more than another and its square is 77 than the square of the smaller number. what are the number?

Answer 1

let small number be x
big number=x+7
(x+7) ^2-x^2=77
x^2+14x+49-x^2=77
14x+49=77
14x=28
x=2
x+7=9
the numbers are 2& 9

Answer 2

Let one number be x and the other be y.

Given, one number is 7 more than another i.e x = y + 7  ----------------- (1)

Given, one number and the other number square is 77 i.e x^2 = y^2 + 77----- (2)

Substitute equation (1) in (2) and on solving we get,

(y + 7)^2 = y^2 + 77

y^2 + 14y = y^2 + 77 - 49

y = 28/14

y  = 2.

Substitute y = 2 in (1), we get

x = 2 + 7

x = 9.

The numbers are x = 9 and y = 2.


Hope this helps!