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Question

Find three numbers in GP such that their sum is 14 and the sum of their square is 84-

A
3,6,12
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B
2,6,18
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C
1,3,9
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D
2,4,8
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Solution

The correct option is D 2,4,8
Let three numbers in G.P=a,ar,ar2
Sum of three number=14
a+ar+ar2=14 ……..(1)
Sum of squares of number=84
a2+a2r2+a2r4=84
Squaring equation (1) both sides
a2+a2r2+a2r4+2a2r+2a2r3+2a2r2=196
84+2a2r(1+r2+r)=196
2a2r14a=19684
2ar14=112
a=11214×2r=4r
4r+4+4r=14
4+4r+4r2=14r
4r210r+4=0
2r25r+2=0
r=5±25164
r=5±34
=2,12
r=2,a=2; r=12,a=8
Three terms: 2,4,8
Three terms: 8,4,2
Three terms are: 2,4,8.

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