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How to find $x,y$ : $2^{x^2+y} + 2^{x + y^2} = 128$ , $\sqrt{x} + \sqrt{y} = 2\sqrt{2}$

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#exponential-function #systems-of-equations #radicals #symmetric-functions
862
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System of equations involving square roots

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#systems-of-equations #radicals #symmetric-functions
965
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An identity about Vandermonde determinant.

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#linear-algebra #polynomials #determinant #symmetric-polynomials #symmetric-functions
238
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Find the value of symmetric function $\sum{\frac{\alpha\beta}{\gamma^2}}$

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#algebra-precalculus #symmetric-functions
69
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Find an equation with the given roots

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#polynomials #roots #symmetric-functions
48
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Is there an easier way to solve this system of equations?

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#systems-of-equations #radicals #symmetric-functions
67
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Expressing positive symmetric function with harmonic functions

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#lie-groups #harmonic-functions #symmetric-functions
306
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Given that $xyz=1$, prove that $\frac{x}{1+x^4}+\frac{y}{1+y^4}+\frac{z}{1+z^4}\le \frac{3}{2}$

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#multivariable-calculus #inequality #contest-math #symmetric-functions #tangent-line-method
167
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Are representations of symmetric groups determined by its restrictions?

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#representation-theory #symmetric-groups #symmetric-functions
224
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Find $x^2+y^2$ if $x^2-\frac{2}{x}=3y^2$ and $y^2-\frac{11}{y}=3x^2$

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#systems-of-equations #rational-functions #symmetric-functions
155
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Inequalities of expressions completely symmetric in their variables

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#inequality #symmetric-polynomials #symmetric-functions
399
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Representation of symmetric function

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#multivariable-calculus #symmetric-polynomials #symmetric-functions
495
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Prove that if $W \subseteq V$ is a subspace s.t. $W \cap W^\perp = \{0\}$, then $V = W\oplus W^\perp$

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#linear-algebra #vector-spaces #bilinear-form #symmetric-functions
71
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Finding out the solution to the system of equations

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#logarithms #systems-of-equations #symmetric-functions
987
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Express power sums in terms of elementary symmetric functions

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#abstract-algebra #polynomials #symmetric-polynomials #symmetric-functions

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