Question

The sum of three numbers which are in A.P is 27and if the sum of the squares of those numbers is 293, find the numbers​

Answer 1

Answer:

let the terms are

a-d, a ,a+d

then

sum is 3a=27

a=9

sum of square =293

.(a-d)^2+a^2+(a+d)^2

=3a^2+2d^2=293

2d^2=293-243

d^2=25

d=+-5

then

no. are

4,9,14

or 14,9,4

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Answer 2

let those no are

a-d ,a,a+d

Step-by-step explanation:

a-d +a +a+ d=27________1

3a=27

a=9__________'2

then

(a-d)²+a²+(a+d)²= 293_________3

now from 2 into 3

(9-d)²+9²+(9+d)² =293

81+81+81+2d² =293

293-243 =2d²

50/2 =d²

√25=d

d=5

so no are

9-5,9,9+5

4,9,14