Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation x+12=5
-
Equation 1-x/2=x/3
-
Equation x^2+x=12
-
Equation x^4=(x-56)^2
- Express {x} in terms of y where:
- 18*x+19*y=7
- 8*x-13*y=-12
- 1*x+6*y=6
- -6*x+1*y=-5
- Derivative of:
-
x^4
- Graphing y =:
- x^4
- Limit of the function:
-
x^4
-
Identical expressions
- x^ four =(x- fifty-six)^ two
- x to the power of 4 equally (x minus 56) squared
- x to the power of four equally (x minus fifty minus six) to the power of two
- x4=(x-56)2
- x4=x-562
- x⁴=(x-56)²
- x to the power of 4=(x-56) to the power of 2
- x^4=x-56^2
-
Similar expressions
- x^4-(50/(z))=14
- x.diff(x)=3*x-3*x^(4/3)*cos(y)
- x^4=(x+56)^2
x^4=(x-56)^2 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation:
$$x^{4} = \left(x - 56\right)^{2}$$
transform:
Take common factor from the equation
$$\left(x - 7\right) \left(x + 8\right) \left(x^{2} - x + 56\right) = 0$$
Because the right side of the equation is zero, then the solution of the equation is exists if at least one of the multipliers in the left side of the equation equal to zero.
We get the equations
$$x - 7 = 0$$
$$x + 8 = 0$$
$$x^{2} - x + 56 = 0$$
solve the resulting equation:
1.
$$x - 7 = 0$$
Move free summands (without x)
from left part to right part, we given:
$$x = 7$$
We get the answer: x1 = 7
2.
$$x + 8 = 0$$
Move free summands (without x)
from left part to right part, we given:
$$x = -8$$
We get the answer: x2 = -8
3.
$$x^{2} - x + 56 = 0$$
This equation is of the form
A quadratic equation can be solved
using the discriminant.
The roots of the quadratic equation:
$$x_{3} = \frac{\sqrt{D} - b}{2 a}$$
$$x_{4} = \frac{- \sqrt{D} - b}{2 a}$$
where D = b^2 - 4*a*c - it is the discriminant.
Because
$$a = 1$$
$$b = -1$$
$$c = 56$$
, then
Because D<0, then the equation
has no real roots,
but complex roots is exists.
or
$$x_{3} = \frac{1}{2} + \frac{\sqrt{223} i}{2}$$
$$x_{4} = \frac{1}{2} - \frac{\sqrt{223} i}{2}$$
The final answer:
$$x_{1} = 7$$
$$x_{2} = -8$$
$$x_{3} = \frac{1}{2} + \frac{\sqrt{223} i}{2}$$
$$x_{4} = \frac{1}{2} - \frac{\sqrt{223} i}{2}$$
$$x^{4} = \left(x - 56\right)^{2}$$
transform:
Take common factor from the equation
$$\left(x - 7\right) \left(x + 8\right) \left(x^{2} - x + 56\right) = 0$$
Because the right side of the equation is zero, then the solution of the equation is exists if at least one of the multipliers in the left side of the equation equal to zero.
We get the equations
$$x - 7 = 0$$
$$x + 8 = 0$$
$$x^{2} - x + 56 = 0$$
solve the resulting equation:
1.
$$x - 7 = 0$$
Move free summands (without x)
from left part to right part, we given:
$$x = 7$$
We get the answer: x1 = 7
2.
$$x + 8 = 0$$
Move free summands (without x)
from left part to right part, we given:
$$x = -8$$
We get the answer: x2 = -8
3.
$$x^{2} - x + 56 = 0$$
This equation is of the form
a*x^2 + b*x + c = 0
A quadratic equation can be solved
using the discriminant.
The roots of the quadratic equation:
$$x_{3} = \frac{\sqrt{D} - b}{2 a}$$
$$x_{4} = \frac{- \sqrt{D} - b}{2 a}$$
where D = b^2 - 4*a*c - it is the discriminant.
Because
$$a = 1$$
$$b = -1$$
$$c = 56$$
, then
D = b^2 - 4 * a * c =
(-1)^2 - 4 * (1) * (56) = -223
Because D<0, then the equation
has no real roots,
but complex roots is exists.
x3 = (-b + sqrt(D)) / (2*a)
x4 = (-b - sqrt(D)) / (2*a)
or
$$x_{3} = \frac{1}{2} + \frac{\sqrt{223} i}{2}$$
$$x_{4} = \frac{1}{2} - \frac{\sqrt{223} i}{2}$$
The final answer:
$$x_{1} = 7$$
$$x_{2} = -8$$
$$x_{3} = \frac{1}{2} + \frac{\sqrt{223} i}{2}$$
$$x_{4} = \frac{1}{2} - \frac{\sqrt{223} i}{2}$$
Sum and product of roots
[src]
sum
_____ _____
1 I*\/ 223 1 I*\/ 223
-8 + 7 + - - --------- + - + ---------
2 2 2 2
$$\left(\left(-8 + 7\right) + \left(\frac{1}{2} - \frac{\sqrt{223} i}{2}\right)\right) + \left(\frac{1}{2} + \frac{\sqrt{223} i}{2}\right)$$
=
0
$$0$$
product
/ _____\ / _____\
|1 I*\/ 223 | |1 I*\/ 223 |
-8*7*|- - ---------|*|- + ---------|
\2 2 / \2 2 /
$$- 56 \left(\frac{1}{2} - \frac{\sqrt{223} i}{2}\right) \left(\frac{1}{2} + \frac{\sqrt{223} i}{2}\right)$$
=
-3136
$$-3136$$
-3136
Rapid solution
[src]
x1 = -8
$$x_{1} = -8$$
x2 = 7
$$x_{2} = 7$$
_____
1 I*\/ 223
x3 = - - ---------
2 2
$$x_{3} = \frac{1}{2} - \frac{\sqrt{223} i}{2}$$
_____
1 I*\/ 223
x4 = - + ---------
2 2
$$x_{4} = \frac{1}{2} + \frac{\sqrt{223} i}{2}$$
x4 = 1/2 + sqrt(223)*i/2
Numerical answer
[src]
x1 = 0.5 - 7.46659226153404*i
x2 = 0.5 + 7.46659226153404*i
x3 = 7.0
x4 = -8.0
x4 = -8.0
The graph