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Question

The value of α so that the geometric mean of x and y, where xy is xα+2+yα+2xα+1+yα+1, is

A
23
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B
14
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C
32
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D
76
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Solution

The correct option is C 32
The G.M between x and y
=xy
Now,
xα+2+yα+2xα+1+yα+1=xyy×(xy)α+2+1(xy)α+1+1=xy(xy)α+2+1(xy)α+1+1=xy
Assuming t=xy, we get
tα+2+1tα+1+1=ttα+2+1tα+3/2t1/2=0(tα+3/21)(t1/21)=0tα+3/2=1 or t=1α=32 or t=1
When t=1, we get
x=y

Hence, α=32

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