Question

A number 15 is divided into 3 parts which are in arithmetic progression and the sum of their square is 83. Find the smallest number? How to find? Plzz help

Answer 1

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 :)

Answer 2

The sum of three parts is 15.

Let the three numbers are a-d,a,a+d(given numbers are in A.P).

=>a-d+a+a+d=15

=>3a=15 (+d and -d will cancel)

=>a=5

Now the sum of squares is 83.

=>(a-d)^2+a^2+(a+d)^2=83

=>a^2+d^2-2ad+a^2+a^2+d^2+2ad=83

=>3a^2+2d^2=83

=>(3×25)+2d^2=83

=>75+2d^2=83

=>2d^2=83-75

=>2d^2=8

=>d^2=4

=>d=+2 or -2

The numbers are 3,5,7.

so the smallest number is 3