Question

The integers x,y and z each are perfect squares and x >y>z>0. If x,y,z from an AP then the smallest possible value of x is​

Answer 1

Given:  3 perfect square numbers x, y and z

To find: The smallest possible value of x?

Solution:

• Now we have given three numbers by following condition:

            x > y > z > 0

            and these numbers are in AP.

• Now lets write all the perfect squares from 1 to 10, they are:

            1, 4, 9, 16, 25, 36, 49, 64, 81, 100

• Now from this, we can see that 25 is half the sum of 1 and 49.

• So the numbers could be 1, 25 and 49

• Let x = 49, z = 1 then:

            x + z / 2 = y

            49 + 1 / 2 = y

            y = 50 / 2

            y = 25

• So the value of y is 25 and x is 49.

Answer:

              Hence, the smallest possible value of x is 49.