Answer:
x = 11
y = 7
Step-by-step explanation:
Let x and y be the unknown numbers.
"The difference between two positive numbers is 4..." (1)
x - y = 4
Assuming that:
x and y ≥ 0
"...the sum of their squares is 170" (2)
x² + y² = 170
Arrange the first equation (1):
x - y = 4
x = 4 + y
Now substitute x to equation (2):
x² + y² = 170
(4 + y)² + y² = 170
y² + 8y + 16 + y² = 170
y² + y² + 8y + 16 = 170
2y² + 8y + 16 = 170
2y² + 8y = 170 - 16
2y² + 8y = 154
2y² + 8y - 154 = 0
Quadratic:
[tex]\frac{-8+\sqrt{8^{2}-4*2(-154) } }{2*2}[/tex] = 7
[tex]\frac{-8-\sqrt{8^{2}-4*2(-154) } }{2*2}[/tex] = -11
Recall that:
x and y ≥ 0 or that it is only positive.
So y = 7
Now solve for x in equation (1):
x = 4 + y
x = 4 + (7)
x = 11
