Discussion
The sum of three numbers in G.P. is 14 and their product is 64. The numbers are:
Answer: B
Let the numbers be \(a/r, a, ar\). Their product is \(a^3 = 64\), so \(a=4\). Their sum is \(a/r + a + ar = 14 \Rightarrow 4/r + 4 + 4r = 14 \Rightarrow 4/r + 4r = 10 \Rightarrow 4+4r^2=10r \Rightarrow 4r^2-10r+4=0 \Rightarrow 2r^2-5r+2=0 \Rightarrow (2r-1)(r-2)=0\). So \(r=2\) or \(r=1/2\). If r=2, numbers are 2, 4, 8. If r=1/2, numbers are 8, 4, 2.
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