Mister Exam
Other calculators
-
How to use it?
- Equation:
- Equation x^4-35*x^2-36=0
-
Equation sin(x)=pi/2
- Equation x^2-49=0
-
Equation 3*sin(x)=0
- Express {x} in terms of y where:
- 18*x+19*y=7
- 1*x+6*y=6
- -16*x-12*y=12
- -17*x-12*y=-9
- Graphing y =:
- sqrt(2x-1)
- sqrt(1-2x)
- Integral of d{x}:
-
sqrt(2x-1)
- sqrt(1-2x)
- Derivative of:
-
sqrt(2x-1)
-
sqrt(1-2x)
-
Identical expressions
- sqrt(2x- one)=sqrt(one -2x)
- square root of (2x minus 1) equally square root of (1 minus 2x)
- square root of (2x minus one) equally square root of (one minus 2x)
- √(2x-1)=√(1-2x)
- sqrt2x-1=sqrt1-2x
-
Similar expressions
- (sqrt(1-2*x))*(ln(16*(x*x)-(a*a)))=(sqrt(1-2*x))*(ln(4*x+a))
- sqrt(2x+1)=sqrt(1-2x)
- sqrt(2*x+15)-sqrt(2*x-1)=2*x+9
- sqrt(2x-1)=sqrt(1+2x)
- sqrt(1-2*x)=a-abs(7)
- tg(2*arccos(sqrt(1-2(x^2))))
- sqrt(x^2-36)=sqrt(2*x-1)
sqrt(2x-1)=sqrt(1-2x) equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
_________ _________ \/ 2*x - 1 = \/ 1 - 2*x
$$\sqrt{2 x - 1} = \sqrt{1 - 2 x}$$
Detail solution
Given the equation
$$\sqrt{2 x - 1} = \sqrt{1 - 2 x}$$
We raise the equation sides to 2-th degree
$$2 x - 1 = 1 - 2 x$$
Move free summands (without x)
from left part to right part, we given:
$$2 x = 2 - 2 x$$
Move the summands with the unknown x
from the right part to the left part:
$$4 x = 2$$
Divide both parts of the equation by 4
We get the answer: x = 1/2
check:
$$x_{1} = \frac{1}{2}$$
$$- \sqrt{1 - 2 x_{1}} + \sqrt{2 x_{1} - 1} = 0$$
=
$$- \sqrt{1 - 1} + \sqrt{-1 + \frac{2}{2}} = 0$$
=
- the identity
The final answer:
$$x_{1} = \frac{1}{2}$$
$$\sqrt{2 x - 1} = \sqrt{1 - 2 x}$$
We raise the equation sides to 2-th degree
$$2 x - 1 = 1 - 2 x$$
Move free summands (without x)
from left part to right part, we given:
$$2 x = 2 - 2 x$$
Move the summands with the unknown x
from the right part to the left part:
$$4 x = 2$$
Divide both parts of the equation by 4
x = 2 / (4)
We get the answer: x = 1/2
check:
$$x_{1} = \frac{1}{2}$$
$$- \sqrt{1 - 2 x_{1}} + \sqrt{2 x_{1} - 1} = 0$$
=
$$- \sqrt{1 - 1} + \sqrt{-1 + \frac{2}{2}} = 0$$
=
0 = 0
- the identity
The final answer:
$$x_{1} = \frac{1}{2}$$
Sum and product of roots
[src]
sum
1/2
$$\frac{1}{2}$$
=
1/2
$$\frac{1}{2}$$
product
1/2
$$\frac{1}{2}$$
=
1/2
$$\frac{1}{2}$$
1/2