Question

8)
Three numbers are in A.P, their sum is 30 and
sum of their squares is 350, Find them,​

Answer 1

$\huge\tt\underline\red{given-}$

three term are in ap

their sum is 30

sum of their square is 350

$\huge\tt\underline\pink{to - find}$

determine ap

$\huge\tt\underline\green{let- the- ap}$

a-d ,a ,a+d

$\huge\tt\underline\purple{solution}$

sum is 30

a-d+a+a+d=30

3a=30

a=10. equation (1)

sum of their square is 350

(a-d)^2 + a^2+(a+d)^2=350

a^2 + d^2-2ad+a^2+a^2+d^2+2ad=350

3(a)^2+2(d)^2=350

put value of a from equation (1)

3(10)^2+2(d)^2=350

300+2d^2=350

2d^2=350-300

2d^2=50

d^2=25

d=√25

d=±5

value of a=10

value of d=5

numbers are

1)

=a-d

=10-5

=5

2)second number

a=10

3)third number

a+d

=10+5

=15

[hence,ap is 5,10,15 ,,,,,,,,,,,,,,]

$\huge\tt\underline\pink{thanks}$

$\huge\tt\underline\orange{hope -its -helpful}$