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jamal1425
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#1
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#1
The coefficeint of x³ in the expanison of (2 + x)(3-ax)4 (to the power of 4)
is 30. Find the values of the constant a.

Thanks in advance.
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Jonny W
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Report 14 years ago
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Coefficient of x^2 in (3 - ax)^4: 4C2 3^2 (-a)^2 = 54a^2
Coefficient of x^3 in (3 - ax)^4: 4C3 3 (-a)^3 = -12a^3

Coefficient of x^3 in (2 + x)(3 - ax)^4: 2*(-12a^3) + 54a^2 = -24a^3 + 54a^2

30 = -24a^3 + 54a^2
24a^3 - 54a^2 + 30 = 0
4a^3 - 9a^2 + 5 = 0
(a - 1)(4a^2 - 5a - 5) = 0
a = 1 or a = (1/8)(5 +- sqrt(105))
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misshn
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#3
Report 14 years ago
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(Original post by jamal1425)
The coefficeint of x³ in the expanison of (2 + x)(3-ax)4 (to the power of 4)
is 30. Find the values of the constant a.

Thanks in advance.
(2+x)(3-ax)^4 = (2+x)(3^4 - 4.3^3.ax + 6.3^2.(ax)^2 - 4.3.(ax)^3 + (ax)^4) = P(x) + (54a^2 -24a^3).x^3

So 54a^2 - 24a^3 = 30 =>9a^2-4a^3=6
=>4a^3 - 9a^2 +6 = 0=>(a-1)(4a^2-5a-5)=0
=>a= 1 or (5 +/- square root of 105)/8
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