Question 604876: two numbers are related in this way:
the number 1 is subtracted from the first number, the difference is squared, then doubled;the result is equal to the second number. the number 1 is added to the first number, and the sum is squared;the result is equal to 4 minus the second number. determine the numbers.
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! two numbers are related in this way
x & y
:
Step-by-step
the number 1 is subtracted from the first number, the difference is squared,
(x-1)^2
:
then doubled;
2(x-1)^2
;
the result
2(x^2-2x+1) = 2x^2 - 4x + 2
:
is equal to the second number.
2x^2 - 4x + 2 = y
:
the number 1 is added to the first number, and the sum is squared;
(x+1)^2 = x^2 + 2x + 1
:
the result is equal to 4 minus the second number
x^2 + 2x + 1 = 4 - y
x^2 + 2x + 1 - 4 = -y
x^2 + 2x - 3 = -y
2x^2 - 4x + 2 = +y; add the 1st equation
-----------------eliminates y
3x^2 - 2x - 1 = 0
Factors to
(3x+1)(x-1) = 0
Two solutions
x = 1
and
3x = -1
x = -.333
:
find y when x = 1
y = 2(1-1)^2
y = 0
:
Find y when x = -.333
y = 2(-.333-1)^2
y = 2(1.77)
y = 3.54
:
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