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phymatter
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What is the expansion of x^{n} +y^{n} , when is even ??/
elibj123 said:I don't see anything that can be expanded.
phymatter said:What is the expansion of x^{n} +y^{n} , when is even ??/
phymatter said:i mean that x^{n} - y^{n} can be written as (x-y)(x^{n-1} +x^{n-2}y ...+y^{n-1} )
similarly what can x^{n} +y^{n} be written as ?
The formula for solving X^n + y^n is (X+y)(X^(n-1) - X^(n-2)y + X^(n-3)y^2 - ... + y^(n-1)). This is known as the binomial theorem and can be used to expand and simplify this equation.
Yes, X and y can be any type of number, including integers, fractions, decimals, and irrational numbers. The equation will work as long as both X and y are raised to the same power, n.
To solve for X and y in this equation, you can use the quadratic formula. First, rearrange the equation to be in the form (X^n + y^n) = 0. Then, substitute X^n = -y^n and solve for X. This will give you two possible values for X, which you can then plug back into the original equation to solve for y.
Solving X^n + y^n is important in mathematics because it helps us understand the relationship between different types of numbers, such as integers and irrational numbers. It also allows us to manipulate and simplify complex equations, making them easier to solve and understand.
Yes, there are many real-world applications for solving X^n + y^n. One example is in physics, where this equation can be used to calculate the magnitude of vector quantities. This equation is also used in engineering and computer science, as well as in financial calculations such as compound interest.