Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation sinx=1
-
Equation cosx=1/2
-
Equation sqrt(x)+1=x-1
- Equation 11*x=2/11
- Express {x} in terms of y where:
- 12*10^(-30)-0,1884*10^12*x^2-y(0,3768*10^12*x+1,183152*10^12*x^3)+y^2(2,760688*10^24*x^2)=0=0
- (x^2+y^2)×(x+y-3)=2xy
- sqrt(1-x)^2+(4-y)^2=0
- lnx+sin(y/x+2x)=4
-
Identical expressions
- (fifteen -x)^(zero . seventy-five)= thirteen . nine
- (15 minus x) to the power of (0.75) equally 13.9
- (fifteen minus x) to the power of (zero . seventy minus five) equally thirteen . nine
- (15-x)(0.75)=13.9
- 15-x0.75=13.9
- 15-x^0.75=13.9
-
Similar expressions
- (15+x)^(0.75)=13.9
(15-x)^(0.75)=13.9 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
3/4 139
(15 - x) = ---
10
$$\left(15 - x\right)^{\frac{3}{4}} = \frac{139}{10}$$
Detail solution
Given the equation
$$\left(15 - x\right)^{\frac{3}{4}} = \frac{139}{10}$$
Because equation degree is equal to = 3/4 - does not contain even numbers in the numerator, then
the equation has single real root.
We raise the equation sides to 4/3-th degree:
We get:
$$\left(\left(15 - x\right)^{\frac{3}{4}}\right)^{\frac{4}{3}} = \left(\frac{139}{10}\right)^{\frac{4}{3}}$$
or
$$15 - x = \frac{139 \cdot 10^{\frac{2}{3}} \sqrt[3]{139}}{100}$$
Expand brackets in the right part
Move free summands (without x)
from left part to right part, we given:
$$- x = -15 + \frac{139 \cdot 10^{\frac{2}{3}} \sqrt[3]{139}}{100}$$
Divide both parts of the equation by -1
We get the answer: x = 15 - 139*10^(2/3)*139^(1/3)/100
The final answer:
$$x_{1} = - \frac{139 \cdot 10^{\frac{2}{3}} \sqrt[3]{139}}{100} + 15$$
$$\left(15 - x\right)^{\frac{3}{4}} = \frac{139}{10}$$
Because equation degree is equal to = 3/4 - does not contain even numbers in the numerator, then
the equation has single real root.
We raise the equation sides to 4/3-th degree:
We get:
$$\left(\left(15 - x\right)^{\frac{3}{4}}\right)^{\frac{4}{3}} = \left(\frac{139}{10}\right)^{\frac{4}{3}}$$
or
$$15 - x = \frac{139 \cdot 10^{\frac{2}{3}} \sqrt[3]{139}}{100}$$
Expand brackets in the right part
15 - x = 139*10^2/3*139^1/3/100
Move free summands (without x)
from left part to right part, we given:
$$- x = -15 + \frac{139 \cdot 10^{\frac{2}{3}} \sqrt[3]{139}}{100}$$
Divide both parts of the equation by -1
x = -15 + 139*10^(2/3)*139^(1/3)/100 / (-1)
We get the answer: x = 15 - 139*10^(2/3)*139^(1/3)/100
The final answer:
$$x_{1} = - \frac{139 \cdot 10^{\frac{2}{3}} \sqrt[3]{139}}{100} + 15$$
Sum and product of roots
[src]
sum
2/3 3 _____
139*10 *\/ 139
15 - -----------------
100
$$- \frac{139 \cdot 10^{\frac{2}{3}} \sqrt[3]{139}}{100} + 15$$
=
2/3 3 _____
139*10 *\/ 139
15 - -----------------
100
$$- \frac{139 \cdot 10^{\frac{2}{3}} \sqrt[3]{139}}{100} + 15$$
product
2/3 3 _____
139*10 *\/ 139
15 - -----------------
100
$$- \frac{139 \cdot 10^{\frac{2}{3}} \sqrt[3]{139}}{100} + 15$$
=
2/3 3 _____
139*10 *\/ 139
15 - -----------------
100
$$- \frac{139 \cdot 10^{\frac{2}{3}} \sqrt[3]{139}}{100} + 15$$
15 - 139*10^(2/3)*139^(1/3)/100
Rapid solution
[src]
2/3 3 _____
139*10 *\/ 139
x1 = 15 - -----------------
100
$$x_{1} = - \frac{139 \cdot 10^{\frac{2}{3}} \sqrt[3]{139}}{100} + 15$$
x1 = -139*10^(2/3)*139^(1/3)/100 + 15