(a) Three numbers are in the ratio 6:7:8 and their sum is 189. Find the numbers
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Answered by
1
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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