Mister Exam
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How to use it?
- Equation:
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Equation (x^2-1)/(x+2)=4x
-
Equation 3*x+5+(x+5)=(1-x)+4
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Equation cos(x)=3/4
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Equation cos(x)=(1/2)
- Express {x} in terms of y where:
- 18*x-20*y=-7
- -13*x+7*y=11
- -19*x-14*y=-8
- -8*x-15*y=15
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Identical expressions
- sqrt2*(cosx-sinx)- one = zero
- square root of 2 multiply by ( co sinus of e of x minus sinus of x) minus 1 equally 0
- square root of 2 multiply by ( co sinus of e of x minus sinus of x) minus one equally zero
- √2*(cosx-sinx)-1=0
- sqrt2(cosx-sinx)-1=0
- sqrt2cosx-sinx-1=0
- sqrt2*(cosx-sinx)-1=O
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Similar expressions
- sqrt2*(cosx-sinx)+1=0
- sqrt2*(cosx+sinx)-1=0
sqrt2*(cosx-sinx)-1=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
___ \/ 2 *(cos(x) - sin(x)) - 1 = 0
$$\sqrt{2} \left(- \sin{\left(x \right)} + \cos{\left(x \right)}\right) - 1 = 0$$
Rapid solution
[src]
/ ___ ___ ___\ x1 = 2*atan\-2 + \/ 2 + \/ 3 - \/ 6 /
$$x_{1} = 2 \operatorname{atan}{\left(- \sqrt{6} - 2 + \sqrt{2} + \sqrt{3} \right)}$$
/ ___ ___ ___\ x2 = -2*atan\2 + \/ 3 - \/ 2 - \/ 6 /
$$x_{2} = - 2 \operatorname{atan}{\left(- \sqrt{6} - \sqrt{2} + \sqrt{3} + 2 \right)}$$
x2 = -2*atan(-sqrt(6) - sqrt(2) + sqrt(3) + 2)
Sum and product of roots
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sum
/ ___ ___ ___\ / ___ ___ ___\ 2*atan\-2 + \/ 2 + \/ 3 - \/ 6 / - 2*atan\2 + \/ 3 - \/ 2 - \/ 6 /
$$2 \operatorname{atan}{\left(- \sqrt{6} - 2 + \sqrt{2} + \sqrt{3} \right)} - 2 \operatorname{atan}{\left(- \sqrt{6} - \sqrt{2} + \sqrt{3} + 2 \right)}$$
=
/ ___ ___ ___\ / ___ ___ ___\ - 2*atan\2 + \/ 3 - \/ 2 - \/ 6 / + 2*atan\-2 + \/ 2 + \/ 3 - \/ 6 /
$$2 \operatorname{atan}{\left(- \sqrt{6} - 2 + \sqrt{2} + \sqrt{3} \right)} - 2 \operatorname{atan}{\left(- \sqrt{6} - \sqrt{2} + \sqrt{3} + 2 \right)}$$
product
/ ___ ___ ___\ / ___ ___ ___\ 2*atan\-2 + \/ 2 + \/ 3 - \/ 6 /*-2*atan\2 + \/ 3 - \/ 2 - \/ 6 /
$$2 \operatorname{atan}{\left(- \sqrt{6} - 2 + \sqrt{2} + \sqrt{3} \right)} \left(- 2 \operatorname{atan}{\left(- \sqrt{6} - \sqrt{2} + \sqrt{3} + 2 \right)}\right)$$
=
/ ___ ___ ___\ / ___ ___ ___\ -4*atan\-2 + \/ 2 + \/ 3 - \/ 6 /*atan\2 + \/ 3 - \/ 2 - \/ 6 /
$$- 4 \operatorname{atan}{\left(- \sqrt{6} - 2 + \sqrt{2} + \sqrt{3} \right)} \operatorname{atan}{\left(- \sqrt{6} - \sqrt{2} + \sqrt{3} + 2 \right)}$$
-4*atan(-2 + sqrt(2) + sqrt(3) - sqrt(6))*atan(2 + sqrt(3) - sqrt(2) - sqrt(6))
Numerical answer
[src]
x1 = -1.83259571459405
x2 = 25.3945406165175
x3 = -56.2868683768171
x4 = -39.5317075576716
x5 = 29.5833308213039
x6 = 6.54498469497874
x7 = -75.1364242983559
x8 = -144.251462677331
x9 = -58.3812634792103
x10 = -77.2308194007491
x11 = -12.30457122656
x12 = -62.5700536839967
x13 = 17.0169602069447
x14 = 73.565627971561
x15 = -24.8709418409192
x16 = 19.1113553093379
x17 = 0.261799387799149
x18 = -177.761784315622
x19 = 67.2824426643814
x20 = 10.7337748997651
x21 = -87.7027949127151
x22 = 81.9432083811338
x23 = 69.3768377667746
x24 = 243.21163126541
x25 = 4.45058959258554
x26 = 50.5272818452358
x27 = 48.4328867428426
x28 = -43.720497762458
x29 = -26.9653369433124
x30 = -37.4373124552784
x31 = -89.7971900151083
x32 = -70.9476340935695
x33 = -68.8532389911763
x34 = 44.2440965380563
x35 = 42.1497014356631
x36 = 54.7160720500222
x37 = -31.1541271480988
x38 = 79.8488132787406
x39 = 23.3001455141243
x40 = -20.6821516361328
x41 = -83.5140047079287
x42 = -14.3989663289532
x43 = 94.5095789954929
x44 = -18.5877565337396
x45 = -100.269165527074
x46 = 56.8104671524154
x47 = -52.0980781720307
x48 = -45.8148928648512
x49 = -33.248522250492
x50 = 63.093652459595
x51 = -81.4196096055355
x52 = 98.6983692002793
x53 = -6.02138591938044
x54 = -50.0036830696375
x55 = 37.9609112308767
x56 = 60.9992573572018
x57 = 100.792764302673
x58 = 88.2263936883134
x59 = 92.4151838930998
x60 = -8.11578102177363
x61 = 31.6777259236971
x62 = 35.8665161284835
x63 = 75.6600230739542
x64 = 86.1319985859202
x65 = 12.8281700021583
x66 = -64.6644487863899
x67 = -93.9859802198946
x68 = -96.0803753222878
x68 = -96.0803753222878