Question

Find 4 numbers in AP whose sum is 2 and the product of the first and last number is equal to 10 times the product of their two medians?

Answer 1

let four no. are in ap be a-b, a,a+d,a+2d
a-d+a+a+d+a+2d=2
4a+2d=2
2a+d=1 (i)
(a-d)(a+2d)= 10 [a×(a+d)]
a^2+2ad-ad-2d^2= 10 [a^2+ad]
a^2+ad-2d^2=10a^2+10 ad
a^2-9a^2+ad-10ad-2d^2=0
-8a^2-9ad-2d^2 = 0
8a^2+9ad+2d^2=0
solve this equation