√(1-x) +√(12+x) -5=0
slove the following equations
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maths question
2007-09-25 6:44 pm
回答 (2)
2007-09-25 7:12 pm
✔ 最佳答案
As follows:圖片參考：http://i117.photobucket.com/albums/o61/billy_hywung/Sep07/Crazyquadratic23.jpg
After checking by direct substitution, both x = -8 and x = -3 are valid inputs for the original equation.
參考: My Maths knowledge
2007-09-25 7:23 pm
√(12+x) = 5 - √(1-x)
12+x = 25 - 10√(1-x) + (1-x) (squaring both sides)
10√(1-x) = 26 - x -12 - x
10√(1-x) = 14 - 2x
100(1-x) = 196 - 56x + 4x" (squaring both sides again, x" = x square)
100 -100x = 196 - 56x + 4x"
4x" + 44x + 96 = 0
x" + 11x + 24 = 0
(x + 3)(x + 8) = 0
x = -3 or x = -8
12+x = 25 - 10√(1-x) + (1-x) (squaring both sides)
10√(1-x) = 26 - x -12 - x
10√(1-x) = 14 - 2x
100(1-x) = 196 - 56x + 4x" (squaring both sides again, x" = x square)
100 -100x = 196 - 56x + 4x"
4x" + 44x + 96 = 0
x" + 11x + 24 = 0
(x + 3)(x + 8) = 0
x = -3 or x = -8
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