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Resources tagged with AM/GM inequality similar to About Pythagorean Golden Means:

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Broad Topics > Advanced Algebra > AM/GM inequality

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About Pythagorean Golden Means

Stage: 5

What is the relationship between the arithmetic, geometric and harmonic means of two numbers, the sides of a right angled triangle and the Golden Ratio?

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Classical Means

Stage: 5 Short Challenge Level: Challenge Level:1

Use the diagram to investigate the classical Pythagorean means.

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Three Ways

Stage: 5 Challenge Level: Challenge Level:1

If x + y = -1 find the largest value of xy by coordinate geometry, by calculus and by algebra.

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Without Calculus

Stage: 5 Challenge Level: Challenge Level:1

Given that u>0 and v>0 find the smallest possible value of 1/u + 1/v given that u + v = 5 by different methods.