f4 amaths (2 questions)

2007-09-26 9:31 pm
Solve the following equations.
√(1-x) + √(12+x) – 5 = 0
If α and β are the roots of the equation 2x2 + 5x -4 = 0, find the values of the following expressions.
α3β – αβ3

回答 (1)

2007-09-26 9:50 pm
✔ 最佳答案
√(1-x) + √(12+x) – 5 = 0
√(1-x) + √(12+x)=5
(√(1-x) + √(12+x))^2=25
1-x+2乘√(1-x)乘√(12+x)+(12+x)=25
13+2乘√(1-x)乘√(12+x)=25
2乘√(1-x)乘√(12+x)=12
√(1-x)乘√(12+x)=6
(1-x)(12+x)=36
12-11x-x^2=36
x^2+11x+24=0
(x+3)(x+8)=0
so x= -3 or x= -8


α+β= -5/2
αβ= -4/2 = -2

α3β – αβ3
=αβ(α^2-β^2)
=αβ(α+β)(α-β)

α-β=√(α-β)^2
=√((α+β)^2-4αβ)
=√(25/4+8)
=√(57/4)
所以αβ(α+β)(α-β)= (-2)(-5/2)(√(57/4))
參考: 自己


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