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If a ,b >0 such that a^3+b^3=2, then sho...

If `a ,b >0` such that `a^3+b^3=2,` then show that `a+blt=2.`

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Verified by Experts

We have
`((a^(3))^(1//3) + (b^(3))^(1//3))/(2) le (a^(3 + b^(3))/(2))^(1//3)`
`implies (a + b)/(2) le 1`
`implies a + b le 2`
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