amaths問一問

Q1 (x^2+5x)^2-8(x^2+5x)-84=0
Ans:
Let y=(x^2+5x),
(x^2+5x)^2-8(x^2+5x)-84=0
y^2-8y-84=0
(y-14)(y+6)=0
y=14 or y= -6
x^2+5x=14 or x^2+5x=-6
x^2+5x-14=0 or x^2+5x+6=0
(x+7)(x-2)=0 or (x+3)(x+2)=0
x=-7 , x=2 , x=-3 , x=-2//
So. x= -7 , -3 , -2 , 2.

Q2 x^(2/3)-13x^(1/3)+36=0
Ans:
Lets x^(1/3)=y
x^(2/3)-13x^(1/3)+36=0
y^2-13y+36=0
(y-9)(y-4)=0
y=9 or y= 4
x^(1/3)=9 or (x^1/3)=4
x=9^3 or x=4^3
x=729 or 64//


Q3 x^-2-x^-1-56=0
let x^-1 = y
x^-2-x^-1-56=0
y^2-y-56=0
(y-8)(y+7)=0
y=8 or y=-7
x^-1=8 or x^-1=-7
x=1/8 or x= -1/7//

Q4 (3x+7)(x-1)=4(x-1)
(3x+7)(x-1)-4(x-1)=0
(x-1)(3x+7-4)=0
(x-1)(3x+3)=0
(x-1)(x+1)=0
x=1 or x=-1//

1.設y=(x^2+5x)
y^2-8y-84=0
(y+6)(y-14)=0
y=-6 or y=14
當y=-6
x^2+5x=-6
x^2+5x+6=0
(x+2)(x+3)=0
x=-2orx=-3
當y=14
x^2+5x=14
x^2+5x-14=0
(x+7)(x-2)=0
x=-7or x=2

2.設y=x^1/3
y^2-13x+36=0
(y-4)(y-9)=0
y=4 or y=9
當y=4,
x^1/3=4
(x^1/3)^3=4^3
x=64
當y=9
x^1/3=9
(x^1/3)^3=9^3
x=729

3.設y=x^-1
y^2-y-56=0
(y+7)(y-8)=0
y=-7 or y=8
當y=-7,
x^-1=-7
(x^-1)^-1=(-7)^-1
x=-1/7
當y=8
x^-1=8
(x^-1)^-1=8^-1
x=1/8

4.(3x+7)(x-1)=4(x-1)
3x^2+4x-7=4x-4
3x^2-3=0
3(x^2-1)=0
x^2-1=0
(x+1)(x-1)=0
x=-1 or x=1