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 The set of all real numbers x  for which x2|x+2|+x>0 is

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By Expert Faculty of Sri Chaitanya
a
(−∞,−2)
b
(−∞,−2)∪(2,∞)
c
(−∞,−1)∪(1,∞)
d
(2,∞)

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detailed solution

Correct option is B

Case I: x+2≥0 or x≥−2∴ x2−2>0⇒ (x−2)(x+2)>0⇒ x<−2 or x>2∴ x∈[−2,−2)∪(2,∞)-----(1) Case II: x+2<0 or x<−2∴ x2+2x+2>0, which is true for real x . ∴ x∈(−∞,−2)----(2)From (1) and (2),x∈(−∞,−2)∪(2,∞)


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