Minimum of a Cubic Sum

★ 6/10Extrema algebra inequality Vieta's Formulas Symmetry

Problem

Real numbers $a, b, c$ satisfy

a + b + c = 1, \qquad a^2 + b^2 + c^2 = 1.

Find the minimum value of $a^3 + b^3 + c^3$ .

Answer

Solution

Difficulty	6/10
Topics	Extrema, algebra, inequality, Vieta's Formulas, Symmetry

Whiteboard

Your sketch is saved only in this browser. To share it, export your drawing as an image (whiteboard menu → Export as → PNG), then upload that image in the comments below.

Discussion

Ask questions, share alternate solutions, and use LaTeX freely.

0 comments

No comments yet.