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- La ecuación:
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Ecuación 6*x^2+x-7=0
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Ecuación 2-5(3+2x)=17
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Ecuación (6*x+8)/2+5=5*x/3
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Ecuación 2,6x-0,75=0,9x-35,6
- Expresar {x} en función de y en la ecuación:
- -9*x-12*y=-19
- -8*x+3*y=-4
- 10*x+3*y=2
- -10*x-12*y=-10
-
Expresiones idénticas
- sqrt(9x+ cien)-(sqrt^ cuatro (9x+ cien))= dos
- raíz cuadrada de (9x más 100) menos ( raíz cuadrada de en el grado 4(9x más 100)) es igual a 2
- raíz cuadrada de (9x más cien) menos ( raíz cuadrada de en el grado cuatro (9x más cien)) es igual a dos
- √(9x+100)-(√^4(9x+100))=2
- sqrt(9x+100)-(sqrt4(9x+100))=2
- sqrt9x+100-sqrt49x+100=2
- sqrt(9x+100)-(sqrt⁴(9x+100))=2
- sqrt9x+100-sqrt^49x+100=2
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Expresiones semejantes
- sqrt(9x+100)-(sqrt^4(9x-100))=2
- sqrt(9x-100)-(sqrt^4(9x+100))=2
- sqrt(9x+100)+(sqrt^4(9x+100))=2
-
Expresiones con funciones
- Raíz cuadrada sqrt
- sqrt(x-16)=2
- sqrt(5x)-sgrt(14-x)=8
- sqrt(x^2-1)*(x^2+2*x+2)=sqrt(x^2-1)
- sqrt(2x-8)=3
- Sqrt[x+8]-x+2=0
- Raíz cuadrada sqrt
- sqrt(x-16)=2
- sqrt(5x)-sgrt(14-x)=8
- sqrt(x^2-1)*(x^2+2*x+2)=sqrt(x^2-1)
- sqrt(2x-8)=3
- Sqrt[x+8]-x+2=0
sqrt(9x+100)-(sqrt^4(9x+100))=2 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
4 ___________ ___________ \/ 9*x + 100 - \/ 9*x + 100 = 2
$$- \left(\sqrt{9 x + 100}\right)^{4} + \sqrt{9 x + 100} = 2$$
Respuesta rápida
[src]
____________________________________________________________________________________________________
/ | / / ______\ \ |
/ | | |3*\/ 6063 | | |
/ | | atan|----------| | |
/ | | \ 997 / pi| |
/ | 16*cos|- ---------------- + --| |
/ | 16 \ 3 3 / 2 |
___________________________________________________________________________________ I* / |- --- - ------------------------------- + ------------------------------------------------------|
/ __________________________ / | 243 243 _________________________________________|
/ / ______ / | / / / ______\ \ |
/ 8 / 997 I*\/ 6063 32 / | / | |3*\/ 6063 | | |
/ - --- + 2*3 / - --------- + ---------- + ------------------------------------- / | / | atan|----------| | |
/ 243 \/ 229582512 76527504 __________________________ / | / | \ 997 / pi| |
/ / ______ / | / 16*cos|- ---------------- + --| |
/ / 997 I*\/ 6063 / | / 8 \ 3 3 / |
/ 59049*3 / - --------- + ---------- / | 729* / - --- + ------------------------------- |
100 \/ \/ 229582512 76527504 \/ | \/ 243 243 |
x1 = - --- + --------------------------------------------------------------------------------------------- - -----------------------------------------------------------------------------------------------------------------------
9 2 2
$$x_{1} = - \frac{100}{9} - \frac{i \sqrt{\left|{- \frac{16}{243} - \frac{16 \cos{\left(- \frac{\operatorname{atan}{\left(\frac{3 \sqrt{6063}}{997} \right)}}{3} + \frac{\pi}{3} \right)}}{243} + \frac{2}{729 \sqrt{- \frac{8}{243} + \frac{16 \cos{\left(- \frac{\operatorname{atan}{\left(\frac{3 \sqrt{6063}}{997} \right)}}{3} + \frac{\pi}{3} \right)}}{243}}}}\right|}}{2} + \frac{\sqrt{- \frac{8}{243} + \frac{32}{59049 \sqrt[3]{- \frac{997}{229582512} + \frac{\sqrt{6063} i}{76527504}}} + 2 \sqrt[3]{- \frac{997}{229582512} + \frac{\sqrt{6063} i}{76527504}}}}{2}$$
____________________________________________________________________________________________________
/ | / / ______\ \ |
/ | | |3*\/ 6063 | | |
/ | | atan|----------| | |
/ | | \ 997 / pi| |
/ | 16*cos|- ---------------- + --| |
/ | 16 \ 3 3 / 2 |
___________________________________________________________________________________ I* / |- --- - ------------------------------- + ------------------------------------------------------|
/ __________________________ / | 243 243 _________________________________________|
/ / ______ / | / / / ______\ \ |
/ 8 / 997 I*\/ 6063 32 / | / | |3*\/ 6063 | | |
/ - --- + 2*3 / - --------- + ---------- + ------------------------------------- / | / | atan|----------| | |
/ 243 \/ 229582512 76527504 __________________________ / | / | \ 997 / pi| |
/ / ______ / | / 16*cos|- ---------------- + --| |
/ / 997 I*\/ 6063 / | / 8 \ 3 3 / |
/ 59049*3 / - --------- + ---------- / | 729* / - --- + ------------------------------- |
100 \/ \/ 229582512 76527504 \/ | \/ 243 243 |
x2 = - --- + --------------------------------------------------------------------------------------------- + -----------------------------------------------------------------------------------------------------------------------
9 2 2
$$x_{2} = - \frac{100}{9} + \frac{\sqrt{- \frac{8}{243} + \frac{32}{59049 \sqrt[3]{- \frac{997}{229582512} + \frac{\sqrt{6063} i}{76527504}}} + 2 \sqrt[3]{- \frac{997}{229582512} + \frac{\sqrt{6063} i}{76527504}}}}{2} + \frac{i \sqrt{\left|{- \frac{16}{243} - \frac{16 \cos{\left(- \frac{\operatorname{atan}{\left(\frac{3 \sqrt{6063}}{997} \right)}}{3} + \frac{\pi}{3} \right)}}{243} + \frac{2}{729 \sqrt{- \frac{8}{243} + \frac{16 \cos{\left(- \frac{\operatorname{atan}{\left(\frac{3 \sqrt{6063}}{997} \right)}}{3} + \frac{\pi}{3} \right)}}{243}}}}\right|}}{2}$$
x2 = -100/9 + sqrt(-8/243 + 32/(59049*(-997/229582512 + sqrt(6063)*i/76527504)^(1/3)) + 2*(-997/229582512 + sqrt(6063)*i/76527504)^(1/3))/2 + i*sqrt(Abs(-16/243 - 16*cos(-atan(3*sqrt(6063)/997)/3 + pi/3)/243 + 2/(729*sqrt(-8/243 + 16*cos(-atan(3*sqrt(6063)/997)/3 + pi/3)/243))))/2
Suma y producto de raíces
[src]
suma
____________________________________________________________________________________________________ ____________________________________________________________________________________________________
/ | / / ______\ \ | / | / / ______\ \ |
/ | | |3*\/ 6063 | | | / | | |3*\/ 6063 | | |
/ | | atan|----------| | | / | | atan|----------| | |
/ | | \ 997 / pi| | / | | \ 997 / pi| |
/ | 16*cos|- ---------------- + --| | / | 16*cos|- ---------------- + --| |
/ | 16 \ 3 3 / 2 | / | 16 \ 3 3 / 2 |
___________________________________________________________________________________ I* / |- --- - ------------------------------- + ------------------------------------------------------| ___________________________________________________________________________________ I* / |- --- - ------------------------------- + ------------------------------------------------------|
/ __________________________ / | 243 243 _________________________________________| / __________________________ / | 243 243 _________________________________________|
/ / ______ / | / / / ______\ \ | / / ______ / | / / / ______\ \ |
/ 8 / 997 I*\/ 6063 32 / | / | |3*\/ 6063 | | | / 8 / 997 I*\/ 6063 32 / | / | |3*\/ 6063 | | |
/ - --- + 2*3 / - --------- + ---------- + ------------------------------------- / | / | atan|----------| | | / - --- + 2*3 / - --------- + ---------- + ------------------------------------- / | / | atan|----------| | |
/ 243 \/ 229582512 76527504 __________________________ / | / | \ 997 / pi| | / 243 \/ 229582512 76527504 __________________________ / | / | \ 997 / pi| |
/ / ______ / | / 16*cos|- ---------------- + --| | / / ______ / | / 16*cos|- ---------------- + --| |
/ / 997 I*\/ 6063 / | / 8 \ 3 3 / | / / 997 I*\/ 6063 / | / 8 \ 3 3 / |
/ 59049*3 / - --------- + ---------- / | 729* / - --- + ------------------------------- | / 59049*3 / - --------- + ---------- / | 729* / - --- + ------------------------------- |
100 \/ \/ 229582512 76527504 \/ | \/ 243 243 | 100 \/ \/ 229582512 76527504 \/ | \/ 243 243 |
- --- + --------------------------------------------------------------------------------------------- - ----------------------------------------------------------------------------------------------------------------------- + - --- + --------------------------------------------------------------------------------------------- + -----------------------------------------------------------------------------------------------------------------------
9 2 2 9 2 2
$$\left(- \frac{100}{9} - \frac{i \sqrt{\left|{- \frac{16}{243} - \frac{16 \cos{\left(- \frac{\operatorname{atan}{\left(\frac{3 \sqrt{6063}}{997} \right)}}{3} + \frac{\pi}{3} \right)}}{243} + \frac{2}{729 \sqrt{- \frac{8}{243} + \frac{16 \cos{\left(- \frac{\operatorname{atan}{\left(\frac{3 \sqrt{6063}}{997} \right)}}{3} + \frac{\pi}{3} \right)}}{243}}}}\right|}}{2} + \frac{\sqrt{- \frac{8}{243} + \frac{32}{59049 \sqrt[3]{- \frac{997}{229582512} + \frac{\sqrt{6063} i}{76527504}}} + 2 \sqrt[3]{- \frac{997}{229582512} + \frac{\sqrt{6063} i}{76527504}}}}{2}\right) + \left(- \frac{100}{9} + \frac{\sqrt{- \frac{8}{243} + \frac{32}{59049 \sqrt[3]{- \frac{997}{229582512} + \frac{\sqrt{6063} i}{76527504}}} + 2 \sqrt[3]{- \frac{997}{229582512} + \frac{\sqrt{6063} i}{76527504}}}}{2} + \frac{i \sqrt{\left|{- \frac{16}{243} - \frac{16 \cos{\left(- \frac{\operatorname{atan}{\left(\frac{3 \sqrt{6063}}{997} \right)}}{3} + \frac{\pi}{3} \right)}}{243} + \frac{2}{729 \sqrt{- \frac{8}{243} + \frac{16 \cos{\left(- \frac{\operatorname{atan}{\left(\frac{3 \sqrt{6063}}{997} \right)}}{3} + \frac{\pi}{3} \right)}}{243}}}}\right|}}{2}\right)$$
=
___________________________________________________________________________________
/ __________________________
/ / ______
200 / 8 / 997 I*\/ 6063 32
- --- + / - --- + 2*3 / - --------- + ---------- + -------------------------------------
9 / 243 \/ 229582512 76527504 __________________________
/ / ______
/ / 997 I*\/ 6063
/ 59049*3 / - --------- + ----------
\/ \/ 229582512 76527504
$$- \frac{200}{9} + \sqrt{- \frac{8}{243} + \frac{32}{59049 \sqrt[3]{- \frac{997}{229582512} + \frac{\sqrt{6063} i}{76527504}}} + 2 \sqrt[3]{- \frac{997}{229582512} + \frac{\sqrt{6063} i}{76527504}}}$$
producto
/ ____________________________________________________________________________________________________\ / ____________________________________________________________________________________________________\ | / | / / ______\ \ | | | / | / / ______\ \ | | | / | | |3*\/ 6063 | | | | | / | | |3*\/ 6063 | | | | | / | | atan|----------| | | | | / | | atan|----------| | | | | / | | \ 997 / pi| | | | / | | \ 997 / pi| | | | / | 16*cos|- ---------------- + --| | | | / | 16*cos|- ---------------- + --| | | | / | 16 \ 3 3 / 2 | | | / | 16 \ 3 3 / 2 | | | ___________________________________________________________________________________ I* / |- --- - ------------------------------- + ------------------------------------------------------| | | ___________________________________________________________________________________ I* / |- --- - ------------------------------- + ------------------------------------------------------| | | / __________________________ / | 243 243 _________________________________________| | | / __________________________ / | 243 243 _________________________________________| | | / / ______ / | / / / ______\ \ | | | / / ______ / | / / / ______\ \ | | | / 8 / 997 I*\/ 6063 32 / | / | |3*\/ 6063 | | | | | / 8 / 997 I*\/ 6063 32 / | / | |3*\/ 6063 | | | | | / - --- + 2*3 / - --------- + ---------- + ------------------------------------- / | / | atan|----------| | | | | / - --- + 2*3 / - --------- + ---------- + ------------------------------------- / | / | atan|----------| | | | | / 243 \/ 229582512 76527504 __________________________ / | / | \ 997 / pi| | | | / 243 \/ 229582512 76527504 __________________________ / | / | \ 997 / pi| | | | / / ______ / | / 16*cos|- ---------------- + --| | | | / / ______ / | / 16*cos|- ---------------- + --| | | | / / 997 I*\/ 6063 / | / 8 \ 3 3 / | | | / / 997 I*\/ 6063 / | / 8 \ 3 3 / | | | / 59049*3 / - --------- + ---------- / | 729* / - --- + ------------------------------- | | | / 59049*3 / - --------- + ---------- / | 729* / - --- + ------------------------------- | | | 100 \/ \/ 229582512 76527504 \/ | \/ 243 243 | | | 100 \/ \/ 229582512 76527504 \/ | \/ 243 243 | | |- --- + --------------------------------------------------------------------------------------------- - -----------------------------------------------------------------------------------------------------------------------|*|- --- + --------------------------------------------------------------------------------------------- + -----------------------------------------------------------------------------------------------------------------------| \ 9 2 2 / \ 9 2 2 /
$$\left(- \frac{100}{9} - \frac{i \sqrt{\left|{- \frac{16}{243} - \frac{16 \cos{\left(- \frac{\operatorname{atan}{\left(\frac{3 \sqrt{6063}}{997} \right)}}{3} + \frac{\pi}{3} \right)}}{243} + \frac{2}{729 \sqrt{- \frac{8}{243} + \frac{16 \cos{\left(- \frac{\operatorname{atan}{\left(\frac{3 \sqrt{6063}}{997} \right)}}{3} + \frac{\pi}{3} \right)}}{243}}}}\right|}}{2} + \frac{\sqrt{- \frac{8}{243} + \frac{32}{59049 \sqrt[3]{- \frac{997}{229582512} + \frac{\sqrt{6063} i}{76527504}}} + 2 \sqrt[3]{- \frac{997}{229582512} + \frac{\sqrt{6063} i}{76527504}}}}{2}\right) \left(- \frac{100}{9} + \frac{\sqrt{- \frac{8}{243} + \frac{32}{59049 \sqrt[3]{- \frac{997}{229582512} + \frac{\sqrt{6063} i}{76527504}}} + 2 \sqrt[3]{- \frac{997}{229582512} + \frac{\sqrt{6063} i}{76527504}}}}{2} + \frac{i \sqrt{\left|{- \frac{16}{243} - \frac{16 \cos{\left(- \frac{\operatorname{atan}{\left(\frac{3 \sqrt{6063}}{997} \right)}}{3} + \frac{\pi}{3} \right)}}{243} + \frac{2}{729 \sqrt{- \frac{8}{243} + \frac{16 \cos{\left(- \frac{\operatorname{atan}{\left(\frac{3 \sqrt{6063}}{997} \right)}}{3} + \frac{\pi}{3} \right)}}{243}}}}\right|}}{2}\right)$$
=
________________________________________________________________
/ / ______\ \ / _____________________ 3 ___
| |3*\/ 6063 | | ___ / 2/3 3 / ______ 128*\/ 2
|atan|----------| | 50*\/ 6 * / -16 + 2 *\/ -997 + 3*I*\/ 6063 + ------------------------
| \ 997 / pi| / _____________________ _____________________
4*sin|---------------- + --| / 3 / ______ ___ 2/3 3 / ______ 3 ___
30002 \ 3 6 / \/ \/ -997 + 3*I*\/ 6063 \/ 6 2 *\/ -997 + 3*I*\/ 6063 16*\/ 2
----- + ---------------------------- - -------------------------------------------------------------------------------- - ---------------------------------------------- + ----------------------------- + ----------------------------
243 243 243 ___________________________________ 1944 _____________________
/ / / ______\ \ 3 / ______
/ | |3*\/ 6063 | | 243*\/ -997 + 3*I*\/ 6063
/ |atan|----------| |
/ | \ 997 / pi|
648* / -1 + 2*sin|---------------- + --|
\/ \ 3 6 /
$$- \frac{\sqrt{6}}{648 \sqrt{-1 + 2 \sin{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{6063}}{997} \right)}}{3} + \frac{\pi}{6} \right)}}} + \frac{4 \sin{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{6063}}{997} \right)}}{3} + \frac{\pi}{6} \right)}}{243} + \frac{30002}{243} + \frac{16 \sqrt[3]{2}}{243 \sqrt[3]{-997 + 3 \sqrt{6063} i}} - \frac{50 \sqrt{6} \sqrt{-16 + \frac{128 \sqrt[3]{2}}{\sqrt[3]{-997 + 3 \sqrt{6063} i}} + 2^{\frac{2}{3}} \sqrt[3]{-997 + 3 \sqrt{6063} i}}}{243} + \frac{2^{\frac{2}{3}} \sqrt[3]{-997 + 3 \sqrt{6063} i}}{1944}$$
30002/243 + 4*sin(atan(3*sqrt(6063)/997)/3 + pi/6)/243 - 50*sqrt(6)*sqrt(-16 + 2^(2/3)*(-997 + 3*i*sqrt(6063))^(1/3) + 128*2^(1/3)/(-997 + 3*i*sqrt(6063))^(1/3))/243 - sqrt(6)/(648*sqrt(-1 + 2*sin(atan(3*sqrt(6063)/997)/3 + pi/6))) + 2^(2/3)*(-997 + 3*i*sqrt(6063))^(1/3)/1944 + 16*2^(1/3)/(243*(-997 + 3*i*sqrt(6063))^(1/3))
Respuesta numérica
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x1 = -11.0784255440507 + 0.123562730708209*i
x2 = -11.0784255440507 - 0.123562730708209*i
x3 = -11.0784255440507 - 0.12356273070821*i
x4 = -11.0784255440507 + 0.123562730708209*i
x4 = -11.0784255440507 + 0.123562730708209*i