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2018 UNM-PNM Statewide High School Mathematics Contest II Problems/Problem 7

Revision as of 04:48, 20 January 2019 by Timneh (talk | contribs) (Created page with "== Problem == Let <math>a,b</math> be positive real numbers such that <math>\frac{1}{a}+ \frac{1}{b} = 1</math>. Show that <math>(a + b)^{2018}-a^{2018}-b^{2018}>= 2^{2\cdot...")
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Problem

Let $a,b$ be positive real numbers such that $\frac{1}{a}+ \frac{1}{b} = 1$. Show that $(a + b)^{2018}-a^{2018}-b^{2018}>= 2^{2\cdot 2018}-2^{2019}$.


Solution

See also

2018 UNM-PNM Contest II (Problems • Answer Key • Resources)
Preceded by
Problem 6 		Followed by
Problem 8
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10
All UNM-PNM Problems and Solutions
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