2x^2-8x-9=5根号(x^2-4x-3)
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2x^2-8x-9=5根号(x^2-4x-3)
2x^2-8x-9=5根号(x^2-4x-3)
2x^2-8x-9=5根号(x^2-4x-3)
设√(x² -4x-3)=y
2x^2-8x-9=5根号(x^2-4x-3)
2(x²-4x-3)-3=5√(x²-4x-3)
2y²-3=5y
2y²-5y-3=0
(2y+1)(y-3)=0
y1=-1/2 (舍) y2=3
√(x²-4x-3)=3
x²-4x-3=9
x²-4x-12=0
(x+2)(x-6)=0
x1=-2 x2=6
如果本题有什么不明白可以追问,
换元法,设Y=√(X^2-4X-3),于是原方程化为:
2Y^2-5Y-3=0,
(2Y+1)(Y-3)=0,
Y=3或Y=-1/2(舍去)
∴X^2-4X-3=9
X^2-4X-12=0
(X-6)(X+2)=0
X1=6,X2=-2,
经检验都是的根。
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