Question

解方程⑴2x^2-4x+3 √ x^-2x+6=15 ⑵ 3/(x^2-2x-3)=2x^2-4x-1需步骤

Answer 1

(1)

2x²-4x+3√(x²-2x+6)=15

2x²-4x+12+3√(x²-2x+6)-27=0

2(x²-2x+6)+3√(x²-2x+6)-27=0

2[√(x²-2x+6)]²+3√(x²-2x+6)-27=0

令√(x²-2x+6)=t,√(x²-2x+6)=√[(x-1)²+5]>0,因此t>0

方程变为

2t²+3t-27=0

(t-3)(2t+9)=0

t=3或t=-9/2(