Selesaikan {l}{(a+d)(a-d)=-1}{(a+d)(b+c)=-3}

\left\{ \begin{array} { l } { ( a + d ) ( a - d ) = - 1 } \\ { ( a + d ) ( b + c ) = - 3 } \end{array} \right.

Selesaikan untuk a, d, b, c

a\in \mathrm{R}\text{, }d=-\frac{b^{2}+2bc+c^{2}+9}{6\left(b+c\right)}\text{, }b=3\sqrt{a^{2}+1}+3a-c\text{, }c\in \mathrm{R}

a\in \mathrm{R}\text{, }d=-\frac{b^{2}+2bc+c^{2}+9}{6\left(b+c\right)}\text{, }b=-3\sqrt{a^{2}+1}+3a-c\text{, }c\in \mathrm{R}

Kuiz

\left\{ \begin{array} { l } { ( a + d ) ( a - d ) = - 1 } \\ { ( a + d ) ( b + c ) = - 3 } \end{array} \right.

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Integral of \int \frac{-x^2+2x-3}{x^3-x^2+x-1}dx

https://math.stackexchange.com/questions/2984961/integral-of-int-frac-x22x-3x3-x2x-1dx

Your computation is almost correct, but you made a mistake here. Note that \int\dfrac{2}{x^2+1}=2\arctan(x) , but not \int\dfrac{2}{x^2+1}\ne2|x^2+1|

Find an integral \int{\frac{dx}{(x+1)^2(x^2+1)}}

https://math.stackexchange.com/questions/2498520/find-an-integral-int-fracdxx12x21

Hint. The polynomial at the denominator is of degree 4 and you have three parameters. Try with is the following partial fraction decomposition (with four parameters): \frac{1}{(x+1)^2(x^2+1)}=\frac{Ax+B}{x^2+1}+\frac{C}{x+1}+\frac{D}{(x+1)^2}.

Solving nonlinear system with three equations and three variables

https://math.stackexchange.com/q/2399397

Multiply the second equation by 2, the third one by 3 and subtract them from the first one. Then we obtain: (x^2+y^2+z^2)-2(x^2-y^2+2z^2)-3(2x^2+y^2-z^2)=6-2\cdot2 -3\cdot 3 that is -7x^2=-7 ...

System of two symmetric equations

https://math.stackexchange.com/questions/2271917/system-of-two-symmetric-equations

your idea was ok, by AM-GM we get with the first equation 4=\frac{ab+b+c+ca}{3}\geq\sqrt[3]{(abc)^2} from here we get abc\le 8 and with the second equation we obtain: \frac{a+b+c+2}{4}\geq\sqrt[4]{2abc} ...

Hausdorff distance vs. distance of the boundaries

https://math.stackexchange.com/questions/33050/hausdorff-distance-vs-distance-of-the-boundaries

For convex paths, you can parametrize D_1 and D_2 by continuously shrinking the paths towards their centroids; then each pair of points with the same parameters has the required relationship. I ...

How to convert the given set of equations into a symmetric form

https://math.stackexchange.com/questions/2297721/how-to-convert-the-given-set-of-equations-into-a-symmetric-form

One way of doing this is to relate \frac a4 to b and c, separately. First, multiplying the first equation by 2 gives 2\times (3a+2b+c)=2\times0 \Leftrightarrow 6a+4b+2c=0. Subtracting the ...

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