If the 3rd, 4th. 5th and sixth term in the expansion of `(x+alpha)^n` are a,b,c,d respectively, then prove that `((b^2-ac)/(c^2-bd))=(5a)/(3c).`

Explanation

let `t_3 = a`

`t_4 = b`

`t_5 = c`

`t_6 = d`

for the expansion `(x+ alpha)^n`

`t_(r+1)/t_r= (n-r+1)/r* alpha/x`

`t_4/t_3= (n-3+1)/3* alpha/x = b/a = (n-2)/3* alpha/x`

`t_5/t_4= (n-4+1)/4* alpha/x = c/b = (n-3)/4* alpha/x `

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