A number 21 is divided into three parts which are in AP and sum of their squares Is 155. Find the largest number.

Sure, let's solve this step by step.

Given that the three parts are in an arithmetic progression (AP), we can denote them as (a-d), a, and (a+d), where 'a' is the middle term and 'd' is the common difference.

According to the problem, the sum of these three parts is 21. So, we can write the equation as:

(a-d) + a + (a+d) = 21 3a = 21 a = 21 / 3 a = 7

The sum of the squares of these three parts is given as 155. So, we can write the equation as:

(a-d)² + a² + (a+d)² = 155 Substitute a = 7 into the equation, we get:

(7-d)² + 7² + (7+d)² = 155 49 - 14d + d² + 49 + 49 + 14d + d² = 155 2d² + 147 = 155 2d² = 155 - 147 2d² = 8 d² = 8 / 2 d² = 4 d = √4 d = 2 or -2

So, the three parts are 5, 7, and 9. The largest number is 9.