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If a and b are positive integers, is 2*a^(1/3) < (a + b)^(1/3) ?

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Re: If a and b are positive integers, is 2*a^(1/3) < (a + b)^(1/3) ? [#permalink]
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If a and b are positive integers, is 2a^(1/3)< (a+b)^(1/3)?
2a^(1/3)< (a+b)^(1/3)
Since, a and b are both positive integers, we can raise both sides to power 3, we get
2^3 * a < (a+b)
=> 8a < a +b
=> 7a < b
So, we need to find is b > 7a?

(1) 7a < b
Sufficient.

(2) 7a < a + b
=> 7a - a < b
=> 6a < b. We find that b > 6a but from statement 2, we don't whether b>7a.
Not sufficient.