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ranga519
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how to prove that solutions of the following equation are irrational
x^3 + x + 1 = 0
x^3 + x + 1 = 0
ranga519 said:how to prove that solutions of the following equation are irrational
x^3 + x + 1 = 0
An irrational number is a real number that cannot be expressed as a ratio of two integers. This means that it cannot be written as a fraction with a finite number of digits after the decimal point.
One way to prove that a solution of an equation is irrational is by contradiction. This involves assuming that the solution is rational and then showing that this leads to a contradiction. This contradiction then proves that the solution must be irrational.
No, not all solutions of an equation are irrational. Some equations may have rational solutions, such as 2x + 4 = 6, which has a rational solution of x = 1.
Yes, irrational numbers are very useful in real life. They are used in various fields such as mathematics, physics, and engineering. For example, pi (π) is an irrational number that is used in many calculations involving circles and curves.
Knowing that a solution is irrational can help us in various ways. It can help us simplify equations, make more accurate calculations, and understand the relationship between rational and irrational numbers. It can also help us solve problems that involve irrational numbers, such as finding the side length of a square with a given area.