Question

在实数范围内分解因式x^3-x^2-2x+2

1.在实数范围内分解因式x^3-x^2-2x+2
2.计算√(3+√5)
详细过程谢谢.

Answer 1

=(x-1)(x^2-2)
=(x-1)(x-根号2）（x+根号2)

√(3+√5)
=√[2(3+√5)]/2
=√(5+1+2√5)/2
=(√5+1)/根号2
=(根号10+根号2）/2

Answer 2

x^3-x^2-2x+2
=X^2(X-1)-2(X-1)
=(X-1)(X^2-2)

Answer 3

1、x^3-x^2-2x+2
＝x^2(x-1)-2(x-1)
＝(x^2-2)(x-1)
＝(x-根号2)(x+根号2)(x-1)

2、√(3+√5)
＝√[(6+2√5)/2]
＝√[(1+√5)^2/2]
＝(1+√5)/√2
＝√2/2+√10/2

Answer 4

1.
x^3-x^2-2x+2
=(x^3-x^2)-(2x-2)
=x^2(x-1)-2(x-1)
=(x-1)(x^2-2)
=(x-1)(x+√2)(x-√2)
2
√(3+√5)
=√1/2(6+2√5)
=√1/2(√5+1)^2
=(√5+1)/√2
=(√10+√2)/2

Answer 5

1
=x^3+1-(x^2+2x-1)
=(x+1)(x^2-x+1)-(x^2+2x+1-2)
=(x+1)(x^2-x+1)-(x+1)^2+2
=(x+1)(x^2-x+1-x-1)+2
=(x+1)(x^2-2x)+2
=2(x+1)(x-2)+2
2
=√[√（1/2）+√（5/2）]^2
=√1/2+√5/2