Mister Exam
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- Equation:
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Equation x^4=(9x-22)^2
- Equation (3y+2)/(4y^2+y)+(y-3)/(16y^2-1)=3/(4y-1)
- Equation sqrt(4×cos^2+6)+sqrt(4×sin^2+8)=6
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Equation (4cos2x-9sinx-4)lg(-cosx)=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
- (four cos2x-9sinx-4)lg(-cosx)= zero
- (4 co sinus of e of 2x minus 9 sinus of x minus 4)lg( minus co sinus of e of x) equally 0
- (four co sinus of e of 2x minus 9 sinus of x minus 4)lg( minus co sinus of e of x) equally zero
- 4cos2x-9sinx-4lg-cosx=0
- (4cos2x-9sinx-4)lg(-cosx)=O
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Similar expressions
- (4cos2x+9sinx-4)lg(-cosx)=0
- (4cos2x-9sinx+4)lg(-cosx)=0
- (4cos2x-9sinx-4)lg(cosx)=0
(4cos2x-9sinx-4)lg(-cosx)=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
(4*cos(2*x) - 9*sin(x) - 4)*log(-cos(x)) = 0
$$\left(- 9 \sin{\left(x \right)} + 4 \cos{\left(2 x \right)} - 4\right) \log{\left(- \cos{\left(x \right)} \right)} = 0$$
Rapid solution
[src]
x_1 = 0
$$x_{1} = 0$$
x_2 = pi
$$x_{2} = \pi$$
pi / 8 \
x_3 = - -- + I*log|----------|
2 | ____|
\9 - \/ 17 /
$$x_{3} = - \frac{\pi}{2} + i \log{\left(\frac{8}{- \sqrt{17} + 9} \right)}$$
pi / 8 \
x_4 = - -- + I*log|----------|
2 | ____|
\9 + \/ 17 /
$$x_{4} = - \frac{\pi}{2} + i \log{\left(\frac{8}{\sqrt{17} + 9} \right)}$$
Sum and product of roots
[src]
sum
pi / 8 \ pi / 8 \
0 + pi + - -- + I*log|----------| + - -- + I*log|----------|
2 | ____| 2 | ____|
\9 - \/ 17 / \9 + \/ 17 /
$$\left(0\right) + \left(\pi\right) + \left(- \frac{\pi}{2} + i \log{\left(\frac{8}{- \sqrt{17} + 9} \right)}\right) + \left(- \frac{\pi}{2} + i \log{\left(\frac{8}{\sqrt{17} + 9} \right)}\right)$$
=
/ 8 \ / 8 \
I*log|----------| + I*log|----------|
| ____| | ____|
\9 + \/ 17 / \9 - \/ 17 /
$$i \log{\left(\frac{8}{\sqrt{17} + 9} \right)} + i \log{\left(\frac{8}{- \sqrt{17} + 9} \right)}$$
product
pi / 8 \ pi / 8 \
0 * pi * - -- + I*log|----------| * - -- + I*log|----------|
2 | ____| 2 | ____|
\9 - \/ 17 / \9 + \/ 17 /
$$\left(0\right) * \left(\pi\right) * \left(- \frac{\pi}{2} + i \log{\left(\frac{8}{- \sqrt{17} + 9} \right)}\right) * \left(- \frac{\pi}{2} + i \log{\left(\frac{8}{\sqrt{17} + 9} \right)}\right)$$
=
0
$$0$$
Numerical answer
[src]
x1 = -21.9911516507526
x2 = -7.85398163397448 - 0.494932923094527*i
x3 = 0.0
x4 = 72.2566292904768
x5 = -100.530964914873
x6 = 61.261056745001 - 0.494932923094527*i
x7 = -14.1371669411541 - 0.494932923094527*i
x8 = -43.9822971502571
x9 = -26.7035375555132 + 0.494932923094527*i
x10 = -20.4203522483337 - 0.494932923094527*i
x11 = 80.1106126665397 - 0.494932923094527*i
x12 = 43.9822971502571
x13 = 87.9645943005142
x14 = -64.4026493985908 - 0.494932923094527*i
x15 = -58.1194640914112 - 0.494932923094527*i
x16 = -72.2565732281109
x17 = 25.1327412287183
x18 = 29.845130209103 - 0.494932923094527*i
x19 = -87.9645943005142
x20 = 6.28318530717959
x21 = 36.1283155162826 - 0.494932923094527*i
x22 = 94.2477796076938
x23 = 54.9778714378214 - 0.494932923094527*i
x24 = 31.4159265358979
x25 = -50.2654824574367
x26 = 59.6903250868673
x27 = -37.6991118430775
x28 = -18.8495559215388
x29 = 98.9601685880785 - 0.494932923094527*i
x30 = 69.1150383789755
x31 = -51.8362787842316 - 0.494932923094527*i
x32 = 15.7080257745707
x33 = 47.123954571834
x34 = -56.5486677646163
x35 = 21.991151628381
x36 = 23.5619449019235 - 0.494932923094527*i
x37 = -6.28318530717959
x38 = 50.2654824574367
x39 = -15.7079743811629
x40 = 65.9734546779902
x41 = 91.1062493303356
x42 = 17.2787595947439 + 0.494932923094527*i
x43 = -65.9734547500033
x44 = -62.8318530717959
x45 = -70.6858347057703 - 0.494932923094527*i
x46 = -12.5663706143592
x47 = 81.6814089933346
x48 = 67.5442420521806 - 0.494932923094527*i
x49 = -59.6902762206901
x50 = 28.2743274615242
x51 = 37.6991118430775
x52 = 73.8274273593601 - 0.494932923094527*i
x53 = -81.6814089933346
x54 = 75.398223686155
x55 = -94.2477796076938
x56 = -28.2742736622651
x56 = -28.2742736622651
The graph