Question

3×(x+1)^2=12

x^2+3=2根号3x (配方法)
(x-1)(x+2)=12(配方法)
2x^2=3x-2(配方法)
已知x=根号2-1,求x^3+3x^2+x+98(先化简,再求值)

Answer 1

x²+3=2√3x 用配方法解
x²-2√3x+3=0
(x-√3)²=0
x-√3=0
x1=x2=√3

(x-1)(x+2)=12 用配方法解
x²+x-2=12
x²+x=14
x²+x+1/4=14+1/4
(x+1/2)²=57/4
x+1/2=±√(57/4)
x+1/2=±√57/2
x=(-1±√57)/2
x1=(-1+√57)/2
x2=(-1-√57)/2

2x²=3x-2
2x²-3x+2=0
a=2 , b=-3 , c=2
△=b²-4ac
=(-3)²-4×2×2
=9-16
=-7
△=-7﹤0,方程无实数解

x=√2-1 , 先化简,再求值
原式=x³+3x²+x+98
=(x³+2x²+x)+x²+98
=x(x²+2x+1)+x²+98
=x(x+1)²+x²+98
=(√2-1)(√2-1+1)²+(√2-1)²+98
=(√2-1)×(√2)²+2-2√2+1+98
=2(√2-1)+101-2√2
=2√2-2+101-2√2
=99