Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation x^2=-74
-
Equation sqrt(5/15-x)=1
-
Equation x^2+x-42=0
-
Equation x^2-7x-8=0
- Express {x} in terms of y where:
- 14*x-16*y=14
- -10*x+18*y=6
- 4*x+13*y=13
- 17*x-19*y=1
-
Identical expressions
- sqrt(five / fifteen -x)= one
- square root of (5 divide by 15 minus x) equally 1
- square root of (five divide by fifteen minus x) equally one
- √(5/15-x)=1
- sqrt5/15-x=1
- sqrt(5 divide by 15-x)=1
-
Similar expressions
- sqrt(5/15+x)=1
sqrt(5/15-x)=1 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\sqrt{- x + \frac{1}{3}} = 1$$
Because equation degree is equal to = 1/2 - does not contain even numbers in the numerator, then
the equation has single real root.
We raise the equation sides to 2-th degree:
We get:
$$\left(\sqrt{- x + \frac{1}{3}}\right)^{2} = 1^{2}$$
or
$$- x + \frac{1}{3} = 1$$
Move free summands (without x)
from left part to right part, we given:
$$- x = \frac{2}{3}$$
Divide both parts of the equation by -1
We get the answer: x = -2/3
The final answer:
$$x_{1} = - \frac{2}{3}$$
$$\sqrt{- x + \frac{1}{3}} = 1$$
Because equation degree is equal to = 1/2 - does not contain even numbers in the numerator, then
the equation has single real root.
We raise the equation sides to 2-th degree:
We get:
$$\left(\sqrt{- x + \frac{1}{3}}\right)^{2} = 1^{2}$$
or
$$- x + \frac{1}{3} = 1$$
Move free summands (without x)
from left part to right part, we given:
$$- x = \frac{2}{3}$$
Divide both parts of the equation by -1
x = 2/3 / (-1)
We get the answer: x = -2/3
The final answer:
$$x_{1} = - \frac{2}{3}$$
Sum and product of roots
[src]
sum
-2/3
$$\left(- \frac{2}{3}\right)$$
=
-2/3
$$- \frac{2}{3}$$
product
-2/3
$$\left(- \frac{2}{3}\right)$$
=
-2/3
$$- \frac{2}{3}$$
Numerical answer
[src]
x1 = -0.666666666666667
x2 = -0.66666666666667 - 5.61950927106415e-15*i
x3 = -0.666666666666667 - 4.47865852143731e-19*i
x3 = -0.666666666666667 - 4.47865852143731e-19*i
The graph