Question

4x^3-16x^2+15x+2=0,求解

Answer 1

解：方程为4x³-16x²+15x+2=0，化为4x³-16x²+16x-x+2=0，4x(x²-4x+4)-(x-2)=0，4x(x-2)²-(x-2)=0，(x-2)[4x(x-2)-1]=0，(x-2)(4x²-8x-1)=0，4(x-2)(x²-2x-1/4)=0，(x-2)[(x-1)²-5/4]=0，则有x-2=0或(x-1)²-5/4=0，得：x₁=2，x₂=1+√5/2，x₃=1-√5/2

解二元二次方程组

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Answer 2

4x^3-16x^2+15x+2=0
4x^3-16x^2+16x-x+2=0
4x(x-2)^2-(x-2)=0
(4x^2-8x-1)(x-2)=0
4(x^2-2x-1/4)(x-2)=0
((x-1)^2-5/4)(x-2)=0
x1=1±√5/2 x2=2