Question

two numbers differ by 6 the difference of their squares is 120 find the numbers​

Answer 1

Answer:

let 'x' and 'y' be the two numbers

two number differ by 6

x - y = 6

y = x - 6

the differences of thier square root is 120

x^2 - y^2 = 120

plug y = x - 6 into the last equation

x^2 - (x - 6)^2 = 120

by solving we find

x = 13

y=x-6

=13-6

=7

The two numbers are 13 and 7.

Answer 2

Answer:

Let x be the first number and x + 6 be the second .

(x + 6)² - x² = 120 expand and rearrange

x² + 12x + 36 - x² - 120 = 0 simplify

12x + 36 = 120 subtract 36 from each side

12x = 84 divide both sides by 12

x = 7 and x + 6 = 13.