1.

(a) Three numbers are in the ratio 6:7:8 and their sum is 189. Find the numbers​

Answer» ONG>Answer:

Let three numbers in G.P=a,ar,ar

2

Sum of three number=14

a+ar+ar

2

=14 ……..(1)

Sum of squares of number=84

a

2

+a

2

R

2

+a

2

r

4

=84

Squaring EQUATION (1) both sides

a

2

+a

2

r

2

+a

2

r

4

+2A

2

r+2a

2

r

3

+2a

2

r

2

=196

84+2a

2

r(1+r

2

+r)=196

2a

2

r

a

14

=196−84

2ar14=112

a=

14×2r

112

=

r

4

r

4

+4+4r=14

4+4r+4r

2

=14r

4r

2

−10r+4=0

2r

2

−5r+2=0

r=

4

5±

25−16

r=

4

5±3

=2,

2

1

r=2,a=2; r=

2

1

,a=8

Three terms: 2,4,8

Three terms: 8,4,2

∴ Three terms are: 2,4,8.


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