Answer:
-2 and 6
Explanation:
Let "x" and "y" be 2 numbers.
The sum of the two numbers is 4. The mathematical expression is:
x + y = 4
y = 4 - x [1]
The sum of their squares minus three times their product is 76. The mathematical expression is:
x² + y² - 3 x y = 76 [2]
If we substitute [1] in [2], we get:
x² + (4 - x)² - 3 x (4 - x) = 76
x² + 16 - 8 x + x² - 12 x + 3 x² = 76
5 x² - 20 x - 60 = 0
We apply the solving formula for second order equations and we get x₁ = 6 and x₂ = -2.
If we replace these x values in [1], we get:
y₁ = 4 - x₁ = 4 - 6 = -2
y₂ = 4 - x₂ = 4 - (-2) = 6
As a consequence, one of the numbers is 6 and the other is -2.
