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Let solution of inequality (16^((1)/(x))...

Let solution of inequality `(16^((1)/(x)))/2^(x+3)gt1` is `(-oo, a) cup (b, c)` then

A

`a^(2) + b^(2) + 9c^(2) = 25`

B

`a + b + c gt 0`

C

`a^(2) + b^(2) + c^(2) = 17`

D

`a + b + c lt 0`

Text Solution

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The correct Answer is:
A, C, D
`(2^((4)/(x)))/(2^(x+3))gt1`
`2^((4)/(x)-x-3)gt1`
`(4)/(x)-x-3gt0`
`(4-x^(2)-3x)/(x)gt0`
`(x^(2)+3x-4)/(x)lt0`
`((x+4)(x-1))/(x)lt0`
`x in (-oo,-4)cup(0,1)`
`a=-4, b=0, c=1`
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