- #1
chwala
Gold Member
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- Homework Statement
- See attached
- Relevant Equations
- Binomial theorem
part (a)
##(4+3x)^{1.5} = 2^3+ 9x+ \left[\dfrac {1}{2} ⋅ \dfrac {3}{2} ⋅\dfrac {1}{2}⋅\dfrac {1}{2}⋅9x^2\right]+ ...##
##(4+3x)^{1.5}=8+9x+\dfrac {27}{16} x^2+...##part (b)
##x≠-\dfrac {4}{3}##part (c)
##(8+9x+\dfrac {27}{16} x^2+...)(1+ax)^2 = \dfrac{107}{16} x^2##
...
##8a^2+18a+\dfrac {27}{16}=\dfrac{107}{16}##
##8a^2+18a=\dfrac{80}{16}##
##128a^2+288a-80=0##
##8a^2+18a-5=0##
##a_1=0.25##
##a_2= -2.5##
Bingo!
Any other way welcome guys...