Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation (x+6)^2=(15-x)^2
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Equation x^2-6*x+11=0
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Equation (-5x+3)*(-x+6)=0
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Equation 3*x/3=(1-x)/2
- Express {x} in terms of y where:
- -11*x-14*y=6
- 9*x-8*y=-6
- 3*x+2*y=-4
- -8*x+16*y=11
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Identical expressions
- ((- two *sin(x)-sqrt(three)*sin^(two)(x)-sqrt(three)*cos^(two)(x)))/((two +sqrt(three)*sin(x))^(two))= zero
- (( minus 2 multiply by sinus of (x) minus square root of (3) multiply by sinus of to the power of (2)(x) minus square root of (3) multiply by co sinus of e of to the power of (2)(x))) divide by ((2 plus square root of (3) multiply by sinus of (x)) to the power of (2)) equally 0
- (( minus two multiply by sinus of (x) minus square root of (three) multiply by sinus of to the power of (two)(x) minus square root of (three) multiply by co sinus of e of to the power of (two)(x))) divide by ((two plus square root of (three) multiply by sinus of (x)) to the power of (two)) equally zero
- ((-2*sin(x)-√(3)*sin^(2)(x)-√(3)*cos^(2)(x)))/((2+√(3)*sin(x))^(2))=0
- ((-2*sin(x)-sqrt(3)*sin(2)(x)-sqrt(3)*cos(2)(x)))/((2+sqrt(3)*sin(x))(2))=0
- -2*sinx-sqrt3*sin2x-sqrt3*cos2x/2+sqrt3*sinx2=0
- ((-2sin(x)-sqrt(3)sin^(2)(x)-sqrt(3)cos^(2)(x)))/((2+sqrt(3)sin(x))^(2))=0
- ((-2sin(x)-sqrt(3)sin(2)(x)-sqrt(3)cos(2)(x)))/((2+sqrt(3)sin(x))(2))=0
- -2sinx-sqrt3sin2x-sqrt3cos2x/2+sqrt3sinx2=0
- -2sinx-sqrt3sin^2x-sqrt3cos^2x/2+sqrt3sinx^2=0
- ((-2*sin(x)-sqrt(3)*sin^(2)(x)-sqrt(3)*cos^(2)(x)))/((2+sqrt(3)*sin(x))^(2))=O
- ((-2*sin(x)-sqrt(3)*sin^(2)(x)-sqrt(3)*cos^(2)(x))) divide by ((2+sqrt(3)*sin(x))^(2))=0
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Similar expressions
- ((2*sin(x)-sqrt(3)*sin^(2)(x)-sqrt(3)*cos^(2)(x)))/((2+sqrt(3)*sin(x))^(2))=0
- ((-2*sin(x)+sqrt(3)*sin^(2)(x)-sqrt(3)*cos^(2)(x)))/((2+sqrt(3)*sin(x))^(2))=0
- ((-2*sin(x)-sqrt(3)*sin^(2)(x)+sqrt(3)*cos^(2)(x)))/((2+sqrt(3)*sin(x))^(2))=0
- ((-2*sin(x)-sqrt(3)*sin^(2)(x)-sqrt(3)*cos^(2)(x)))/((2-sqrt(3)*sin(x))^(2))=0
- ((-2*sinx-sqrt(3)*sin^(2)(x)-sqrt(3)*cos^(2)(x)))/((2+sqrt(3)*sinx)^(2))=0
((-2*sin(x)-sqrt(3)*sin^(2)(x)-sqrt(3)*cos^(2)(x)))/((2+sqrt(3)*sin(x))^(2))=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
___ 2 ___ 2
-2*sin(x) - \/ 3 *sin (x) - \/ 3 *cos (x)
----------------------------------------- = 0
2
/ ___ \
\2 + \/ 3 *sin(x)/
$$\frac{\left(- \sqrt{3} \sin^{2}{\left(x \right)} - 2 \sin{\left(x \right)}\right) - \sqrt{3} \cos^{2}{\left(x \right)}}{\left(\sqrt{3} \sin{\left(x \right)} + 2\right)^{2}} = 0$$
Sum and product of roots
[src]
sum
2*pi pi - ---- - -- 3 3
$$- \frac{2 \pi}{3} - \frac{\pi}{3}$$
=
-pi
$$- \pi$$
product
-2*pi -pi -----*---- 3 3
$$- \frac{2 \pi}{3} \left(- \frac{\pi}{3}\right)$$
=
2 2*pi ----- 9
$$\frac{2 \pi^{2}}{9}$$
2*pi^2/9
Rapid solution
[src]
-2*pi
x1 = -----
3
$$x_{1} = - \frac{2 \pi}{3}$$
-pi
x2 = ----
3
$$x_{2} = - \frac{\pi}{3}$$
x2 = -pi/3
Numerical answer
[src]
x1 = 30.3687289847013
x2 = -46.0766922526503
x3 = -90.0589894029074
x4 = 74.3510261349584
x5 = 55.5014702134197
x6 = 104.71975511966
x7 = 17.8023583703422
x8 = 85.870199198121
x9 = -57.5958653158129
x10 = -39.7935069454707
x11 = 24.0855436775217
x12 = -83.7758040957278
x13 = 41.8879020478639
x14 = 92.1533845053006
x15 = -26.1799387799149
x16 = 5.23598775598299
x17 = 48.1710873550435
x18 = -70.162235930172
x19 = -2.0943951023932
x20 = -13.6135681655558
x21 = 98.4365698124802
x22 = -63.8790506229925
x23 = 68.0678408277789
x24 = -19.8967534727354
x25 = 4.18879020478639
x25 = 4.18879020478639