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Question

If (2+3)x22x+1+(23)x22x1=223, then x is equal to:

A
1
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B
2
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C
both (a) and (c)
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Solution

The correct option is C both (a) and (c)
23=12+3
the given equation can be expressed as
(2+3)x22x+1+1(2+3)x22x+1=2(2+3) . . .(i)
Let us put y=(2+3)x22x+1, then the eq.(i) can be expressed as
y+(2+3)2y=2(2+3) y22(2+3)y+(2+3)2=0 [y(2+3)]2=0 y=2+3 (2+3)x22x+1=(2+3) x22x+1=1 x(x2)=0 x=0 or 2

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