Question

The difference of two numbers is 3 and the sum of their squares is 65. find the numbers.

Answer 1

Eg. x is the first number, y is the second number

The equation
x - y = 3
x² + y² = 65

Use subtitution to find y
x - y = 3
x = y + 3

x² + y² = 65
(y + 3)² + y² = 65
y² + 6y + 9 + y² = 65
2y² + 6y - 56 = 0
y² + 3y - 28 = 0
(y + 7)(y - 4) = 0

y = -7 or y = 4

Find x with y
If y = -7
x = y + 3
x = -4

If y = 4
x = y + 3
x = 7

So the numbers are 7 and 4, or -7 and -4

Answer 2

The numbers are 4 and 7
j^2+k^2=65

4^2+7^2=65
16+49=65
65=65
hope i helped