May 9, 2015 · The answers offered so far just introduce $-2xy$ without explaining where it comes from (except as the inverse of $+2xy$). Remark: I am perfectly aware that $$(a + b)^2= a^2 + 2ab + b^2$$ and that one can subtract $2ab$ and it works.

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Oct 7, 2018 · $$2xy ≤ x^2 + y^2$$ I just can end up in $(xy)^{1/2} ≤ (x+y)/2$. And even though I know that this is ...

Jun 29, 2015 · $\frac{dy}{dx}=\frac{x^2+y^2}{2xy} $..(i) This is a homogeneous differential equation because it has homogeneous functions of same degree 2. homogeneous functions are: $(x^2+y^2)$ and $2xy$, both functions have degree 2. Solution of differential equation: Equation (i) can be written as, $\frac{dy}{dx}=\frac{1+\frac{y}{x}}{2(\frac{y}{x})}$..(ii)

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Dec 13, 2019 · Find max of $(3x^2-2xy+3y^2)(3y^2-2yz+3z^2)(3z^2-2xz+3x^2)$ Hot Network Questions Is there still an active cryptographic standard in some developing country that allows the DLP in the multiplicative group of finite fields?

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Whenever you solve a separable ODE, you should begin by identifying any stationary solutions to the equation. Provided you have uniqueness, any other solutions will never cross the stationary solutions, so that all solutions are either completely stationary or can be found by separation of …

Now the polynomial becomes $$ 2X^2+2XY+Y^2-3 $$ and now it is clear that its values are $\ge-3$, because $2X^2+2XY+Y^2$ is positive definite (the conic is an ellipse), having negative discriminant $4-8=-4$. Or you can write it as $$ X^2+(X+Y)^2-3 $$

Jul 17, 2021 · In this case the factorisation becomes, $$ x^2 + y^2 + z^2 - 2xy - 2yz - 2zx = (ix + jy + kz)^2. $$ I didn't know if there was some algebra which obeyed these properties. algebra-precalculus