A calculus problem by Soumava Pal

Calculus Level 2

Find the value of a a to 3 significant figures, so that x x and y y are distinct real solutions to

x + y = 100 π , x y = y x = a . x+y=100\pi, \\ x^y = y^x = a.


The answer is 349.014931.

Soumava Pal by Soumava Pal , 22, India

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2 solutions

Soumava Pal
Feb 21, 2016

We use this to bring the sum of our roots as close to 100 p i 100pi as we want by using the bisection method.

3 Helpful 1 Interesting 1 Brilliant 0 Confused

can you please explain it in detail

Aniket Jain - 4 years, 2 months ago

Ok, so if x+y= 100π, then substitution for y=100π-x into x^y=y^x yields approx 1.01887

Brice Turner - 1 year, 11 months ago

I also found it very helpful to use y=mx in second equation and parameterizing both x and y in terms of m And then solving first equation using bisection method, for m

pranay uniyal - 1 year ago
Ankan Dutta
Mar 2, 2016

The algorithm was 😍👍👌

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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