Suppose is a positive real number such that `a^(5)-a^(3)+a=2`. Then
Suppose is a positive real number such that `a^(5)-a^(3)+a=2`. Then
A. `a^(6)lt2`
B. `2lt a^(6)lt3`
C. `3lt a^(6)lt4`
D. `4lea^(6)`
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Correct Answer - c
`a^(5)-a^(3)a=2,aepsilonR^(+)`
`Let f(a)=a^(5)-a^(3)+a-2, {"Note f"(a) gt0AAa in R}`
`"for"a^(6)=3Rightarrowa=3^(1//6)=1.2 {"use calculator"}`
`"we get" f(1.2)lt 0 and at a=4^(1//6)RightarrowF(4^(1//6))gt0`
so one root in a `in (3,4)`
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