a. Expand (𝑎+𝑏)5. Hence find the coefficient of 𝑥 in the expansion of (4𝑥+2/9𝑥)5
b. The coefficient of 𝑥2 in the expansion of (1+𝑥)n is 45. Given that 𝑛 is a positive integer, find the value of 𝑛.
a.
"+\\dbinom{5}{3}a^2b^3+\\dbinom{5}{4}ab^4++\\dbinom{5}{5}b^5"
"=a^5+5a^4b+10a^3b^2+10a^2b^3+5ab^4+b^5"
"+\\dfrac{10(64)(4)x^3}{81x^2}+\\dfrac{10(16)(8)x^2}{729x^3}+\\dfrac{5(4)(16)x}{6561x^4}"
"+\\dfrac{32x^4}{59049x^5}=1024x^5+\\dfrac{2560x^3}{9}+\\dfrac{2560x}{81}"
"+\\dfrac{1280}{729x}+\\dfrac{320}{6561x^3}+\\dfrac{32}{59049x^5}"
b.
"\\dbinom{n}{2}=45"
"\\dfrac{n(n-1)}{2}=45"
"n(n-1)=90, n>0"
Then "n=10"
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