✔ 最佳答案
1)2x^2 - 20x + 32 + 5√(x^2 -10x+25) = 0
2x^2 - 20x + 50 - 18 + 5√(x^2 -10x+25) = 0
2(x^2 -10x+25) + 5√(x^2 -10x+25) - 18 = 0
Let √(x^2 -10x+25) be y :
2y^2 + 5y - 18 = 0
(2y + 9)(y - 2) = 0
√(x^2 -10x+25) = - 9/2 (rejected)
or √(x^2 -10x+25) = 2
x^2 -10x+25 = 4
x^2 - 10x + 21 = 0
(x - 3)(x - 7) = 0
x = 3 or x = 7
2)x^2 -6x-√(2x^2 -12x-5)=20
2x^2 - 12x - 2√(2x^2 -12x-5) = 40
(2x^2 - 12x - 5) - 2√(2x^2 -12x-5) = 40 - 5
Let y be √(2x^2 -12x-5) :
y^2 - 2y - 35 = 0
(y - 7)(y + 5) = 0
√(2x^2 -12x-5) = 7 or - 5(rejected)開方根無負數
2x^2 - 12x - 5 = 49
x^2 - 6x - 27 = 0
(x - 9)(x + 3) = 0
x = 9 or x = - 3
2010-02-04 22:23:21 補充:
001 的答案 1) x=1/2 or 19/2 是增根,不是原方程的解,經平方後所得的解
有可能是假答案,所以要代入試驗。
2)也是。