Simultaneous Non-Linear Equations

Computer Science Level 4

Given the non-linear system:

3 x 1 − cos ⁡ ( x 2 x 3 ) = 1 2 , x 1 2 − 81 ( x 2 + 0.1 ) 2 + sin ⁡ x 3 = − 1.06 , e − x 1 x 2 + 20 x 3 = 3 − 10 π 3 . \begin{aligned} 3x_1-\cos(x_2x_3)&=\frac{1}{2},\\ x_1^2-81(x_2+0.1)^2+\sin x_3&=-1.06,\\ e^{-x_1x_2}+20x_3&=\frac{3-10\pi}{3}. \end{aligned}

Find the integer closes to Ω \Omega where

Ω = 1000 ∣ x 1 − 2 x 2 + 3 x 3 ∣ . \Omega=1000\left|x_1-2x_2+3x_3\right|.


The answer is 1071.

Tunk-Fey Ariawan by Tunk-Fey Ariawan , 35, Indonesia

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2 solutions

Michael Mendrin
Mar 17, 2014

You know, there's another set of {x1, x2, x3} that satisfies the non-linear set of equations, which would have yielded another "correct" answer of 689. You need to specify which solution set applies.

1 Helpful 0 Interesting 0 Brilliant 0 Confused

I found the set { 1 2 , 0 , − π 6 \frac{1}{2},0,-\frac{\pi}{6} }, can you give me a clue for the other set?

Ronald Overwater - 7 years, 2 months ago

Ahh, sorry. I've just checked it your 'dispute'. Could you please mention another set solution so I can fix the problem. Thanks...

Tunk-Fey Ariawan - 7 years, 2 months ago
Hasmik Garyaka
Oct 28, 2017

exponent gives rational number if x1 or x2=0. I tried x1, then x2. If x2=0, x1=0.5 and x3=-pi/6. No programming.

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