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Question

The set of all real values of x which satisfies (x2)(x3)2(x1)(x2), is

A
[3,4]
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B
[1,4]
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C
[1,3]
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D
[0,3]
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Solution

The correct option is A [3,4]
(x2)(x3)2(x1)(x2)

(i) (x2)(x3)2
x25x+62x25x+40(x1)(x4)0x[1,4] (1)

(ii) 2(x1)(x2)
x23x+22x23x0x(x3)0x(,0][3,) (2)

From equations (1) and (2),
x[3,4]

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