anonymous
  • anonymous
The first three terms in the expansion of (2+ax)^n in ascending powers of x are 32-40x+bx^2. Find the values of the constants n, a and b
Mathematics
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SOLVED
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schrodinger
  • schrodinger
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campbell_st
  • campbell_st
the value of n is 5 since 2^5 = 32 so the expansion is \[(2 + ax)^n =^nC_{r} (2)^{n - r}(ax)^r\] using the expansion with n = 5 and r = 0 you get \[^5C_{0}(2)^5(ax)^0 = 32\] so to find a, find the coefficient of the 2nd term using the expansion where r = 1 \[^5C_{1}(2)^{5 -1}(ax)^1 = 5 \times 2^4 \times ax\] then you have \[5 \times 16 \times ax = 40ax\] now equate the coefficients -40 = 40a therefore a = -1 so your binomial is now \[(2 - x)^5\] to find the value of b, let r = 2 then \[^5C_{2} (2)^{5-2} ( -x)^2\] just evaluate then compare hope this helps
anonymous
  • anonymous
amazing, thanks so much!
campbell_st
  • campbell_st
lol..glad to help

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