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Question

The solution set of the inequality 1x21x2x+2 is (α,β](γ,α)[δ,), then

A
α+β+γ+δ=5
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B
αβγδ=4
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C
βδ=2
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D
αβγ=0
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Solution

The correct options are
A α+β+γ+δ=5
D αβγ=0

1x21x2x+20x(x+2)(x24)2x(x2)x(x2)(x+2)0x2+2xx2+42x2+4xx(x2)(x+2)02x2+6x+4x(x2)(x+2)0x23x4x(x2)(x+2)0x24x+x4x(x2)(x+2)0(x4)(x+1)(x0)(x2)(x+2)0x(2,1)U(0,2)U(4,)α=2β=1γ=0δ=4α+β+γ+δ=4+21=5αβγ=0


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