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Question

If (2x4)3+(4x2)3=(4x+2x6)3, then how many value(s) of x are possible?

A
3
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B
0
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C
2
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D
1
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Solution

The correct option is A 3
Given: (2x4)3+(4x2)3=(4x+2x6)3
Using the identity (x+y)3=x3+y3+3xy(x+y):
(4x+2x6)3=[(2x4)+(4x2)]3=(2x4)3+(4x2)3+3(2x4)(4x2)(2x4+4x2)
(2x+4x6)3=(4x+2x6)3+3(2x4)(4x2)(2x+4x6) (Given)
3(2x4)(4x2)(2x+4x6)=0
2x4=0,4x2=0 or 2x+4x6=0
Consider 2x4=0.
2x=4
2x=22
x=2
Now, consider 4x2=0.
4x=2
22x=22
2x=1
x=12
Now, consider 2x+4x6=0.
2x+22x6=0
22x+(32)2x6=0
(2x)2+3×2x2×2x6=0
2x(2x+3)2(2x+3)=0
(2x2)(2x+3)=0
2x2=0 or 2x+3=0
2x=2 or 2x=3
Since the value of 2x cannot be negative.
2x=2
2x=21
x=1
Thus, there are three possible values of x for the given expression.
Hence, the correct answer is option (1).

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