4After that ?????
Prove that \left(a^{\alpha} +b^{\alpha } \right)^{1/\alpha }<(a^{\beta }+b^{\beta })^{1/\beta }
when a>0,b>0 , \alpha >\beta >0
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4 Answers
4I guess this works out
(aα + bα )1/α ≥ (a + b)1/α
(aβ + bβ )1/β ≥ (a+b)1/β
we can say that (a+b)1/β > (a + b)1/α
29@Manmay..on dividing both sides by bα
This can be written as \left((\frac{a}{b})^{\alpha } + 1 ) \right)^{\frac{1}{\alpha }} = (p^{x} + 1)^{\frac{1}{x }}
where p is a constant = a/b
Now see the Functions..whether it's increasing or decreasing...
looking at the question it seems the function is decreasing for x > 0
