SOLUTION: If 25X square - Y square = (5 X+1/2) ( 5 X-1/2). Find the value of Y.

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Question 1077857: If 25X square - Y square = (5 X+1/2) ( 5 X-1/2). Find the value of Y.
Found 2 solutions by jorel1380, ikleyn:
Answer by jorel1380(3719) About Me  (Show Source):
You can put this solution on YOUR website!
25x²-y²=(5x + 1/2)(5x - 1/2)
In general, x²-y²=(x+y)(x-y). So:
x=25x
y=1/2
The value of y is 1/2. ☺☺☺☺

Answer by ikleyn(52809) About Me  (Show Source):
You can put this solution on YOUR website!
.
If 25X square - Y square = (5 X+1/2) ( 5 X-1/2). Find the value of Y.
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If  25X%5E2+-+Y%5E2 = %285X%2B1%2F2%29%2A%285X-1%2F2%29, as the condition says, then

25X%5E2+-+Y%5E2 = 25X%5E2+-+%281%2F2%29%5E2.


It implies  Y%5E2 = %281%2F2%29%5E2.


Hence,  Y = +/-1%2F2.


Answer.  There are TWO solutions:  Y = 1%2F2 and Y = -1%2F2.