SOLUTION: The difference between the squares of two numbers is 51. Twice the square of the second number subtracted from the square of the first number is 2. Find the numbers.

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Question 930172: The difference between the squares of two numbers is 51. Twice the square of the second number
subtracted from the square of the first number is 2. Find the numbers.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
The difference between the squares of two numbers is 51.
x^2 - y^2 = 51
:
Twice the square of the second number subtracted from the square of the first number is 2.
x^2 - 2y^2 = 2
:
Find the numbers.
subtract the 1st equation from the 2nd equation
x^2 - 2y^2 = 2
x^2 - y^2 = 51
---------------Subtraction eliminates x^2, find y^2
0 - y^2 = -49
y^2 = 49
y = sqrt%2849%29
y = +/-7
Find x using the 1st equation
x^2 - 7^2 = 51
x^2 - 49 = 51
x^2 = 51 + 49
x = sqrt%28100%29
x = +/-10
:
:
Check in the 2nd equation
10^2 - 2(7^2) = 2
100 - 2(49) = 2