Question

If a, b, c≥0 and abc=25. Find the minimum value of a^3+b^3+c^3.

Answer 1

Answer:

according to given identity

a³+b³+c³=3abc

then, a³+b³+c³=3*25

=a³+b³+c³=75

Step-by-step explanation:

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Answer 2

Answer:

The answer is 75.

Hope it helps!

Step-by-step explanation:

We have the formula:

a³+b³+c³-3abc= (a+b+c)(a²+b²+c²-ab-bc-ca)

a³+b³+c³= (a+b+c)(a²+b²+c²-ab-bc-ca) +3abc

For a³+b³+c³ to be minimum, (a+b+c)(a²+b²+c²-ab-bc-ca) must be 0

Therefore, a³+b³+c³≥ 3abc

≥ 3×25

≥ 75