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jeedoubts
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Homework Statement
if the real numbers x,y,z,w satisfy (x2/(n2-1))+(y2/(n2-32))+(z2/(n2-52))+(w2/(n2-72)) for n=2,4,6,8 then prove
x2+y2+z2+w2=36
Homework Equations
The Attempt at a Solution
unable to think of anything?
radou said:Unless I'm missing something, the problem you posted isn't consistent - what do your numbers x, y, z, w satisfy?
You're unable to think of anything? The most obvious starting point is substituting n = 2, n = 4, n = 6, and n = 8, and seeing what you get.jeedoubts said:Homework Statement
if the real numbers x,y,z,w satisfy (x2/(n2-1))+(y2/(n2-32))+(z2/(n2-52))+(w2/(n2-72)) = 1 for n=2,4,6,8 then prove
x2+y2+z2+w2=36
Homework Equations
The Attempt at a Solution
unable to think of anything?
That will give you four different equations in four unknowns -- in other words, exactly what is needed to solve the problem.Mark44 said:Edit: Add "= 1" to make an equation below.
You're unable to think of anything? The most obvious starting point is substituting n = 2, n = 4, n = 6, and n = 8, and seeing what you get.
To prove this equation, we need to show that it holds true for all possible values of x, y, z, and w. This can be done through algebraic manipulation, substitution, or by using the Pythagorean theorem.
This equation is significant because it is a fundamental property of real numbers and has many practical applications in fields such as physics, engineering, and mathematics. It also helps to understand the concept of vectors and their magnitudes.
One example is by using the Pythagorean theorem. We can rewrite the equation as x2+y2+z2 = 36 - w2. Since the Pythagorean theorem states that in a right triangle, the sum of the squares of the two shorter sides is equal to the square of the hypotenuse, we can see that the left side of our equation represents the magnitude of a vector in 3-dimensional space. Therefore, the equation holds true for all real numbers x, y, and z, as long as w is a real number that satisfies w2 ≤ 36.
No, this equation is only true for real numbers. Non-real numbers do not have a concept of magnitude, which is essential for this equation to hold true.
Yes, there are multiple ways to prove this equation, including using geometric properties, trigonometry, and calculus. Different approaches may be more suitable depending on the context and application of the equation.