Solve for x if the numbers are in arithmetic progression 1s

Solve for x if the numbers are in arithmetic progression .

1+sqrtx, 2-sqrtx,1+2sqrtx.

Solution

The three numbers are in arithmetic progression. We also know that for 3 consecutive terms in an AP the sum of the 1st and 3rd numbers is twice the 2nd number.

Using this 1+ 2 sqrt x + 1 + sqrt x = 2*(2- sqrt x)

=> 2+ 3 sqrt x = 4 - 2 sqrt x

=> 2 = 5 sqrt x

=> sqrt x = 2/5

So x = 4/25

X is 4/25