6. Given the equation x1 + x2 + X3 + x4 = 40, where x1, x2, X3, and x4 are integers. How many different solutions does this equation have if... a. .all the variables must be nonnegative? b. ..all the variables must be positive? c. ..x, 2 0, x2 2 1, x3 2 2, and x, 2 3?

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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**Problem 6:**

Given the equation \(x_1 + x_2 + x_3 + x_4 = 40\), where \(x_1, x_2, x_3,\) and \(x_4\) are integers. How many different solutions does this equation have if:

a. ...all the variables must be nonnegative?

b. ...all the variables must be positive?

c. ...\(x_1 \geq 0, x_2 \geq 1, x_3 \geq 2,\) and \(x_4 \geq 3\)?
Transcribed Image Text:**Problem 6:** Given the equation \(x_1 + x_2 + x_3 + x_4 = 40\), where \(x_1, x_2, x_3,\) and \(x_4\) are integers. How many different solutions does this equation have if: a. ...all the variables must be nonnegative? b. ...all the variables must be positive? c. ...\(x_1 \geq 0, x_2 \geq 1, x_3 \geq 2,\) and \(x_4 \geq 3\)?
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