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Salsk061 [2.6K]
3 years ago
7

Solve the equation x^13-2x^12-x^11+2x^10=0 in the real number system

Mathematics
1 answer:
Lemur [1.5K]3 years ago
7 0

Answer:

x= -1,  x=1  and x=2

Step-by-step explanation:

The equation is;

x^{13} -2x^{12} -x^{11} +2x^{10} =0

Using a graph tool to graph the equation and identify the solution you will have;

x= -1,

x=1

x=2

Check answers

when x=2

2^{13}-2(2^{12} )-2^{11} +2(2^{10} )\\\\\\2^{13} -2^1(2^{12} )-2^{11} +2^1(2^{10} )\\\\\\2^{13} -2^{13} -2^{11} +2^{11} =0

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Answer:

The statement in the question is wrong. The series actually diverges.

Step-by-step explanation:

We compute

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Therefore, by the series divergence test, the series \sum_{n=1}^\infty\frac{n^2}{(n+1)^2} diverges.

EDIT: To VectorFundament120, if (x_n)_{n\in\mathbb N} is a sequence, both \lim x_n and \lim_{n\to\infty}x_n are common notation for its limit. The former is not wrong but I have switched to the latter if that helps.

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Double checking your answer:

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