解方程(1)5x^2-1=0(2)x^2-2x=1(3)(x-1)^2=(2-5x)^2 (4)3x^2-根号3x+6分之1=0

Question

解方程(1)5x^2-1=0(2)x^2-2x=1(3)(x-1)^2=(2-5x)^2 (4)3x^2-根号3x+6分之1=0

Answer 1

(1)5x^2-1=0, 5x^2=1, x^2=1/5, x=±√5/5

(2)x^2-2x=1, x^2-2x+1=2, (x-1)²=2, x-1=±√2, x=1±√2

(3)(x-1)^2=(2-5x)^2 , x²-2x+1=4-20x+25x², 24x²-18x+3=0, 8x²-6x+1=0, (2x-1)(4x-1)=0
x①=1/2. x②=1/4.

(4)3x^2-根号3x+6分之1=0, 3x²-x√3+1/6=0, 18x²-x6√3+1=0,
x=[6√3±√(108-72)]/36=[6√3±6]/36=[√3±1]/6
x①=[√3+1]/6.
x②=[√3-1]/6