<PRE><B>Question 930172</B>
 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(49)}}}
y = +/-7
Find x using the 1st equation
x^2 - 7^2 = 51
x^2 - 49 = 51
x^2 = 51 + 49
x = {{{sqrt(100)}}}
x = +/-10
:
:
Check in the 2nd equation
10^2 - 2(7^2) = 2
100 - 2(49) = 2</PRE>