Question

Find four numbers in an A.P such that their sum is 20 and sum of their squares is 120

Answer 1

Answer:

Step-by-step explanation:

sum of 4numbers in ap=20

4/2(2a+(4-1)d)=20

2(2a+(4-1)d)=20

2a+(4-1)d=10=2a+3d

let it be eq 1

sum of their square is 120

a^2+(a+d)^2+(a+2d)^2+(a+3d)^2=120

a^2+a^2+d^2+2ad+a^2+d^2+4ad+a^2+d^2+6ad=120

4a^2+3d^2+12ad=120 eq 2

squaring the first equation

(2a+3d)^2=100

4a^2+9d^2+12ad=100

taking eq 2

100-6d^2=120