Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation 8*x-3*(2*x+1)=2*x+4
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Equation sinx+cosx=0
- Equation z^2-(2+i)z+2i=0
- Equation √3/(2x-11)=1/13
- Express {x} in terms of y where:
- 10*x+9*y=-4
- -15*x-19*y=2
- -11*x-14*y=-19
- -17*x-15*y=-17
- Limit of the function:
- 1/13
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Identical expressions
- √ three /(2x- eleven)= one / thirteen
- √3 divide by (2x minus 11) equally 1 divide by 13
- √ three divide by (2x minus eleven) equally one divide by thirteen
- √3/2x-11=1/13
- √3 divide by (2x-11)=1 divide by 13
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Similar expressions
- √3/(2x+11)=1/13
- 1/(13x+18)=1/(38x-27)
- ((x-1)/(13-1))=((y-0)/(-5-0))
- 1*2*3+2*4*6+4*8*12+7*14*21/1*3*5+2*6*10+4*12*20+7*21*35=×
√3/(2x-11)=1/13 equation
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The solution
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[src]
___ \/ 3 -------- = 1/13 2*x - 11
$$\frac{\sqrt{3}}{2 x - 11} = \frac{1}{13}$$
Detail solution
Given the equation:
$$\frac{\sqrt{3}}{2 x - 11} = \frac{1}{13}$$
Use proportions rule:
From a1/b1 = a2/b2 should a1*b2 = a2*b1,
In this case
so we get the equation
$$13 \sqrt{3} = 2 x - 11$$
$$13 \sqrt{3} = 2 x - 11$$
Expand brackets in the left part
Move the summands with the unknown x
from the right part to the left part:
$$- 2 x + 13 \sqrt{3} = -11$$
Divide both parts of the equation by (-2*x + 13*sqrt(3))/x
We get the answer: x = 11/2 + 13*sqrt(3)/2
$$\frac{\sqrt{3}}{2 x - 11} = \frac{1}{13}$$
Use proportions rule:
From a1/b1 = a2/b2 should a1*b2 = a2*b1,
In this case
a1 = sqrt(3)
b1 = -11 + 2*x
a2 = 1
b2 = 13
so we get the equation
$$13 \sqrt{3} = 2 x - 11$$
$$13 \sqrt{3} = 2 x - 11$$
Expand brackets in the left part
13*sqrt3 = -11 + 2*x
Move the summands with the unknown x
from the right part to the left part:
$$- 2 x + 13 \sqrt{3} = -11$$
Divide both parts of the equation by (-2*x + 13*sqrt(3))/x
x = -11 / ((-2*x + 13*sqrt(3))/x)
We get the answer: x = 11/2 + 13*sqrt(3)/2
Rapid solution
[src]
___
11 13*\/ 3
x1 = -- + --------
2 2
$$x_{1} = \frac{11}{2} + \frac{13 \sqrt{3}}{2}$$
x1 = 11/2 + 13*sqrt(3)/2
Sum and product of roots
[src]
sum
___ 11 13*\/ 3 -- + -------- 2 2
$$\frac{11}{2} + \frac{13 \sqrt{3}}{2}$$
=
___ 11 13*\/ 3 -- + -------- 2 2
$$\frac{11}{2} + \frac{13 \sqrt{3}}{2}$$
product
___ 11 13*\/ 3 -- + -------- 2 2
$$\frac{11}{2} + \frac{13 \sqrt{3}}{2}$$
=
___ 11 13*\/ 3 -- + -------- 2 2
$$\frac{11}{2} + \frac{13 \sqrt{3}}{2}$$
11/2 + 13*sqrt(3)/2