Question

A number 15 is divided into three parts which are in ap and the sum of their squares is 83. Find the smallest number.

Answer 1

$\large \bold{ \underline { \underline{ \: Answer : \: \: \: }}}$

$\to$ Smallest number = 3

$\large \bold{ \underline { \underline{ \: Explanation : \: \: \: }}}$

Let , a - d , a , a + d are the three parts which are in AP

A.T.Q ,

$\to$ a - d + a + a + d = 15

$\to$ 3a = 15

$\to$ a = 5

Now , sum of their squares is 83

$\to$ (a - d)² + a² + (a + d)² = 83

$\to$ a² + d² + a² + a² + d² = 83

$\to$ 3a² + 2d² = 83

$\to$ 3(25) + 2d² = 83

$\to$ 75 + 2d² = 83

$\to$ 2d² = 8

$\to$ d² = 4

$\to$ d = ± 2

Then , the numbers will be 3 , 5 , 7

Therefore , the smallest number is 3

Answer 2

Answer:

hi friend ,

let a-d,a,a+d are the three parts which are in Ap

→given a-d+a+a+d=15

→3a=15

→a=5

now, sum of their squares is 83

→(a-d)²+a²+(a+d)²=83

→a²+d²+a²+a²+d²=83

→3a²+2d²=83

→3(25)+2d²=83

→75+2d²=83

→2d²=8

d²=4

d=±2

then the numbers will be 3,5,7

the least value is 3

I hope this will help u :)