Mister Exam
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How to use it?
- Equation:
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Equation 4x^4-5x^2+1=0
-
Equation z^6=-1
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Equation sin^2((x/4)+(pi/4))*sin^2((x/4)-(pi/4))=0,375sin^2(-(pi/4))
- Equation (x^2-16):(x^3+3x^2+16)=0
- Express {x} in terms of y where:
- 5*x-5*y=20
- 8*x-7*y=-13
- 15*x-15*y=16
- 9*x+18*y=6
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Identical expressions
- sin^ two ((x/ four)+(pi/ four))*sin^ two ((x/ four)-(pi/ four))= zero ,375sin^ two (-(pi/ four))
- sinus of squared ((x divide by 4) plus ( Pi divide by 4)) multiply by sinus of squared ((x divide by 4) minus ( Pi divide by 4)) equally 0,375 sinus of squared ( minus ( Pi divide by 4))
- sinus of to the power of two ((x divide by four) plus ( Pi divide by four)) multiply by sinus of to the power of two ((x divide by four) minus ( Pi divide by four)) equally zero ,375 sinus of to the power of two ( minus ( Pi divide by four))
- sin2((x/4)+(pi/4))*sin2((x/4)-(pi/4))=0,375sin2(-(pi/4))
- sin2x/4+pi/4*sin2x/4-pi/4=0,375sin2-pi/4
- sin²((x/4)+(pi/4))*sin²((x/4)-(pi/4))=0,375sin²(-(pi/4))
- sin to the power of 2((x/4)+(pi/4))*sin to the power of 2((x/4)-(pi/4))=0,375sin to the power of 2(-(pi/4))
- sin^2((x/4)+(pi/4))sin^2((x/4)-(pi/4))=0,375sin^2(-(pi/4))
- sin2((x/4)+(pi/4))sin2((x/4)-(pi/4))=0,375sin2(-(pi/4))
- sin2x/4+pi/4sin2x/4-pi/4=0,375sin2-pi/4
- sin^2x/4+pi/4sin^2x/4-pi/4=0,375sin^2-pi/4
- sin^2((x/4)+(pi/4))*sin^2((x/4)-(pi/4))=O,375sin^2(-(pi/4))
- sin^2((x divide by 4)+(pi divide by 4))*sin^2((x divide by 4)-(pi divide by 4))=0,375sin^2(-(pi divide by 4))
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Similar expressions
- sin^2((x/4)+(pi/4))*sin^2((x/4)-(pi/4))=0,375sin^2((pi/4))
- sin^2((x/4)-(pi/4))*sin^2((x/4)-(pi/4))=0,375sin^2(-(pi/4))
- sin^2((x/4)+(pi/4))*sin^2((x/4)+(pi/4))=0,375sin^2(-(pi/4))
sin^2((x/4)+(pi/4))*sin^2((x/4)-(pi/4))=0,375sin^2(-(pi/4)) equation
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The solution
You have entered
[src]
2/-pi \
3*sin |----|
2/x pi\ 2/x pi\ \ 4 /
sin |- + --|*sin |- - --| = ------------
\4 4 / \4 4 / 8
$$\sin^{2}{\left(\frac{x}{4} - \frac{\pi}{4} \right)} \sin^{2}{\left(\frac{x}{4} + \frac{\pi}{4} \right)} = \frac{3 \sin^{2}{\left(- \frac{\pi}{4} \right)}}{8}$$
Sum and product of roots
[src]
sum
-13*pi -11*pi -7*pi -5*pi -pi pi 5*pi 7*pi ------ + ------ + ----- + ----- + ---- + -- + ---- + ---- 3 3 3 3 3 3 3 3
$$\left(- \frac{13 \pi}{3}\right) + \left(- \frac{11 \pi}{3}\right) + \left(- \frac{7 \pi}{3}\right) + \left(- \frac{5 \pi}{3}\right) + \left(- \frac{\pi}{3}\right) + \left(\frac{\pi}{3}\right) + \left(\frac{5 \pi}{3}\right) + \left(\frac{7 \pi}{3}\right)$$
=
-8*pi
$$- 8 \pi$$
product
-13*pi -11*pi -7*pi -5*pi -pi pi 5*pi 7*pi ------ * ------ * ----- * ----- * ---- * -- * ---- * ---- 3 3 3 3 3 3 3 3
$$\left(- \frac{13 \pi}{3}\right) * \left(- \frac{11 \pi}{3}\right) * \left(- \frac{7 \pi}{3}\right) * \left(- \frac{5 \pi}{3}\right) * \left(- \frac{\pi}{3}\right) * \left(\frac{\pi}{3}\right) * \left(\frac{5 \pi}{3}\right) * \left(\frac{7 \pi}{3}\right)$$
=
8
-175175*pi
-----------
6561
$$- \frac{175175 \pi^{8}}{6561}$$
Rapid solution
[src]
-13*pi
x_1 = ------
3
$$x_{1} = - \frac{13 \pi}{3}$$
-11*pi
x_2 = ------
3
$$x_{2} = - \frac{11 \pi}{3}$$
-7*pi
x_3 = -----
3
$$x_{3} = - \frac{7 \pi}{3}$$
-5*pi
x_4 = -----
3
$$x_{4} = - \frac{5 \pi}{3}$$
-pi
x_5 = ----
3
$$x_{5} = - \frac{\pi}{3}$$
pi
x_6 = --
3
$$x_{6} = \frac{\pi}{3}$$
5*pi
x_7 = ----
3
$$x_{7} = \frac{5 \pi}{3}$$
7*pi
x_8 = ----
3
$$x_{8} = \frac{7 \pi}{3}$$
Numerical answer
[src]
x1 = -42.9350995990605
x2 = -26.1799387799149
x3 = -80.634211442138
x4 = 61.7846555205993
x5 = 17.8023583703422
x6 = -2631.60744615705
x7 = -45.0294947014537
x8 = -89.0117918517108
x9 = -76.4454212373516
x10 = -95.2949771588904
x11 = -82.7286065445312
x12 = 13.6135681655558
x13 = 68.0678408277789
x14 = -93.2005820564972
x15 = 24.0855436775217
x16 = -99.4837673636768
x17 = 63.8790506229925
x18 = 76.4454212373516
x19 = 51.3126800086333
x20 = 32.4631240870945
x21 = 11.5191730631626
x22 = -49.2182849062401
x23 = -11.5191730631626
x24 = -51.3126800086333
x25 = 99.4837673636768
x26 = 82.7286065445312
x27 = 19.8967534727354
x28 = 93.2005820564972
x29 = 57.5958653158129
x30 = -74.3510261349584
x31 = -61.7846555205993
x32 = -55.5014702134197
x33 = 49.2182849062401
x34 = -225.147473507269
x35 = -32.4631240870945
x36 = -38.7463093942741
x37 = -57.5958653158129
x38 = -68.0678408277789
x39 = -5.23598775598299
x40 = 42.9350995990605
x41 = 36.6519142918809
x42 = -13.6135681655558
x43 = 70.162235930172
x44 = -17.8023583703422
x45 = 74.3510261349584
x46 = 30.3687289847013
x47 = 45.0294947014537
x48 = 26.1799387799149
x49 = -30.3687289847013
x50 = 38.7463093942741
x51 = 55.5014702134197
x52 = 86.9173967493176
x53 = 7.33038285837618
x54 = -63.8790506229925
x55 = -24.0855436775217
x56 = -19.8967534727354
x57 = -7.33038285837618
x58 = 95.2949771588904
x59 = -86.9173967493176
x60 = -1.0471975511966
x61 = -359.188760060433
x62 = -70.162235930172
x63 = 80.634211442138
x64 = -36.6519142918809
x65 = 1.0471975511966
x66 = 89.0117918517108
x67 = 5.23598775598299
x67 = 5.23598775598299
The graph