一元二次方程(2)

4
a+b=4/2=2
ab=1/2

a
a/2+b/2
=(a+b)/2
=2/2
=1
(a/2)(b/2)
=(ab)/4
=(1/2)/4
=1/8
x^2-x+1/8=0
8x^2-8x+1=0

b
(1/a)+(1/b)
=(a+b)/(ab)
=2/(1/2)
=4
(1/a)(1/b)
=1/(ab)
=1/(1/2)
=2
x^2-4x+2=0

c
a^2+b^2
=(a+b)^2-2ab
=2^2-2(1/2)
=3
(a^2)(b^2)
=(ab)^2
=(1/2)^2
=1/4
x^2-3x+1/4=0
4x^2-12x+1=0

d
(a/b)+(b/a)
=(a^2+b^2)/ab
=3/(1/2)
=6
(a/b)(b/a)
=1
x^2-6+1=0

5
a+b=1/3
ab=-2/3

a
a^2+b^2
=(a+b)^2-2ab
=(1/9)-2(-2/3)
=13/9

b
(a-2b)+(b-2a)
=(a+b)-2(ab)
=(1/3)-2(-2/3)
=5/3
(a-2b)(b-2a)
=ab-2a^2-2b^2+4ab
=5ab-2(a^2+b^2)
=5(-2/3)-2(13/9)
=-56/9
x^2-(5/3)x-56/9=0
9x^2-15x-56=0

4.
α+β=2，αβ=1/2
α^2+β^2=4－1=3
(a) α/2+β/2=(α+β)/2=1
(α/2)*(β/2)= αβ/4=1/8
x^2－x+1/8=0
8x^2－8x+1=0
(b) 1/α+1/β=(α+β)/( αβ)=4/(1/2)=8
x^2－8x+2=0
(c) α^2β^2=1/4
x^2－2x+(1/4)=0
4x^2－8x+1=0
(d) (α/β)+(β/α)=(α^2+β^2)/(αβ)=3/(1/2)=6
x^2－6x+1=0

5.
α+β=1/3，αβ=－2/3
(a) α^2+β^2
=(α+β)^2－2αβ
=1/9+4/3
=13/9
(b) (α－2β)+( β－2α)=－(α+β)=－1/3
(α－2β)(β－2α)
=αβ－2α^2－2β^2+4αβ
=－2(α^2+β^2)+5αβ
=－2*13/9+5*(－2/3)
=－56/9
x^2－(－1/3)x－56/9=0
9x^2+3x－56=0