How do I solve this equation: square root of x minus 4 = 2 minus x
[From: ] [author: ] [Date: 12-07-05] [Hit: ]
-I dont undrestand your questionIf it is √x - 4 = 2 - xPut x = y²√(y²) - 4 = 2 - y²y - 4 = 2 - y²y² + y - 6 =0y² - 2y + 3y -6 =0y(y-2) +3(y-2) = 0y = 2 or y = -3as x = y²therefore x = 4 or x = 9and if it is√(x - 4) = 2 - xx - 4 = (2 - x)²x - 4 = 4 - 4x + x²x² - 5x + 8 = 0by using quadratic formulaex = (5 + √7i)/2or x = (5 - √7i)/2 where i = √(-1)-sqrt(x - 4) = 2 - x(sqrt(x - 4))^2 = (2 - x)^2x - 4 = 4 - 4*x + x^24 - 4*x + x^2 - x + 4 = 0x^2 - 5*x + 8 = 0a = 1, b = - 5, c = 8b^2 - 4*a*c = 25 - 4*1*8 = - 7x1 = ( - ( - 5) + sqrt( - 7))/2 = 5/2 + i*sqrt(7)/2x2 = 5/2 - i*sqrt(7)/2As the solutions are complex, there arent real solutions!-Interpreted as √x - 4 = 2 - x√x - 4 = 2 - x√x = 6 - x(√x)² = (6 - x)²x = 36 - 12x +x²0 = x² -13x + 360 = (x - 4)(x - 9)x = 4, 9-√(x - 4) = 2 - xx - 4 = (2 - x)²x - 4 = 4 - 4x + x²x² - 5x + 8 = 0Now it should be easy to solve for x.......
x - 4 = 4 - 4x + x^2
x^2 - 5x + 8 = 0
x = (5 +/- sqrt(25 - 32)) / 2
x = (5 +/- sqrt(-7)) / 2
If you know about imaginary numbers, you continue:
x = (5 +/- isqrt(7)) / 2
I hope this information was very helpful.
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I dont undrestand your question
If it is
√x - 4 = 2 - x
Put x = y²
√(y²) - 4 = 2 - y²
y - 4 = 2 - y²
y² + y - 6 =0
y² - 2y + 3y -6 =0
y(y-2) +3(y-2) = 0
y = 2 or y = -3
as x = y²
therefore x = 4 or x = 9
and if it is
√(x - 4) = 2 - x
x - 4 = (2 - x)²
x - 4 = 4 - 4x + x²
x² - 5x + 8 = 0
by using quadratic formulae
x = (5 + √7i)/2 or x = (5 - √7i)/2 where i = √(-1)
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sqrt(x - 4) = 2 - x
(sqrt(x - 4))^2 = (2 - x)^2
x - 4 = 4 - 4*x + x^2
4 - 4*x + x^2 - x + 4 = 0
x^2 - 5*x + 8 = 0
a = 1, b = - 5, c = 8
b^2 - 4*a*c = 25 - 4*1*8 = - 7
x1 = ( - ( - 5) + sqrt( - 7))/2 = 5/2 + i*sqrt(7)/2
x2 = 5/2 - i*sqrt(7)/2
As the solutions are complex, there aren't real solutions!
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Interpreted as √x - 4 = 2 - x
√x - 4 = 2 - x
√x = 6 - x
(√x)² = (6 - x)²
x = 36 - 12x + x²
0 = x² -13x + 36
0 = (x - 4)(x - 9)
x = 4, 9
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√(x - 4) = 2 - x
x - 4 = (2 - x)²
x - 4 = 4 - 4x + x²
x² - 5x + 8 = 0
Now it should be easy to solve for x.
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