Mathematics: HURRY PLEASE! The difference between two positive numbers is 4 and the sum of their squares is 170. What are the numbers? Do not guess or check. Show your work.

HURRY PLEASE! The difference between two positive

QueenMiah16

20.01.2022

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:

$\frac{-8+\sqrt{8^{2}-4*2(-154) } }{2*2}$ = 7

$\frac{-8-\sqrt{8^{2}-4*2(-154) } }{2*2}$ = -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

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