SOLUTION: The difference of two positive numbers is 2 and the sum of their squares is 74. Find the numbers
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Question 100012: The difference of two positive numbers is 2 and the sum of their squares is 74. Find the numbers
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
"The difference of two positive numbers is 2"
one number = x
another number = (x+2)
:
"the sum of their squares is 74."
x^2 + (x+2)^2 = 74
:
x^2 + (x^2 + 4x + 4) = 74; FOILed (x+2)*(x+2)
:
2x^2 + 4x + 4 - 74 = 0
:
2x^2 + 4x - 70 = 0; a quadratic equation
:
x^2 + 2x - 35; simplified, divided by 2
:
Factors to:
(x + 7) (x - 5) = 0
x = +5, they want the positive number, the other number would be 7
:
:
Check: 5^2 + 7^2 = 74; confirms our solution
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