Which of the following interval(s) satisfy the inequality x20āx11+x6āx3+1>0
A
(−∞,−2)
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B
(2,∞)
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C
(−∞,1)
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D
(0,∞)
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Solution
The correct option is D(0,∞) Case (i): x<0 x<0→(x20−x11)++(x6−x3)+>0 ∴x<0 satisfies.
Case (ii): x>1 x>1→(x20−x11)++(x6−x3)+>0 ∴x>1 satisfies.
Case (iii): 0<x<1 0<x<1→(1−x3)++(x6−x11)++x20+>0 ∴0<x<1 satisfies.
So the given equation is satisfied for ∀x∈R