sum of 3 numbers in ap is 6 and sum of their squares is 14 find the numbers Question sum of 3 numbers in ap is 6 and sum of their squares is 14 find the numbers in progress 0 Math Allison 1 month 2021-08-23T04:29:59+00:00 2021-08-23T04:29:59+00:00 2 Answers 0 views 0

## Answers ( )

Answer:let the three numbers in A. P are:-

(a-d), a, (a+d)

sum of three numbers

a-d+a+a+d=6

3a =6

a=2

sum of their squares

a^2 +(a-d) ^2 +(a+d) ^2=14

2^2 +(2-d)^2 +(2+d)^2 =14

4+4+d^2 – 4d+4+d^2 +4d=14

12+2d^2 =14

2d^2 =2

d^2 =1

d=root1=+-1 d has two values +1,-1

the number are:-

if d=+1

a-d=2-(1)=1

a=2

a+d=2+1=3

if d=-1

a-d=2-(-1)=3

a=2

a+d=2+(-1)=1

Answer:1,2,and3 are the numbers

Step-by-step explanation:1+4+9=14

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