If 3rd, 4th, 5th terms in the expansion of `(a+x)^n` be 84, 280 and 560, Find x, a and n.

Explanation

`T_{3}=\ ^{n} C_{2} x^{n-2} A^{2}`

`T_{4}=\ ^{n} C_{3} x^{n-3} A^{3}`

`T_{5}=\ ^{n} C_{4} x^{n-4} A^{4}`

Now, `frac{T_{4}}{T_{4}}=frac{84}{280}`

`Rightarrow frac{\ ^{n} C_{2} x^{n-2} A^{2}}{\ ^{2} C_{3} x^{n-3} A^{3}}=frac{3}{10}`

`Rightarrow frac{3}{10}=frac{3}{\ ^{n-2}} frac{x}{A} quad ldots(1)`

Similarly, `frac{T_{1}}{T_{4}}=frac{560}{280}`

`Rightarrow frac{n-3}{4} cdot frac{A}{x}=frac{2}{1} quad ldots(2)`

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