How many are you expecting ? How will you know if we give you all of them,
or only some of them ?
Since the highest power of the variable in the equation is '2', ("x2"),
the equation has exactly two solutions.
25x2 - 100 = 0
Divide each side by 25:
x2 - 4 = 0
Add 4 to each side:
x2 = 4
Take the square root of each side:
x = +4 and -4
And there are your two solutions.
No. Some have two solutions where as some have none.
the Bratu's equation is a differential equation which is non-linear (such as, if we have some solutions for it, a linear combinaison of these solutions will not be everytime a solution). It's given by the equation y''+a*e^y=0 or d²y/dy² =-ae^y.
7
The roots of an equation means the solutions of an equation. Different methods have been developed for different kinds of equation. It is not possible to give an overview in one or two paragraphs, but in simpler cases, the same operation is done on both sides of the equation, with the aim of "isolating" the variable you are solving for, that is, having it alone on one side. In some complicated cases, no "explicit" solutions exist, and "numerical" solutions have to be used; this basically means using trial-and-error.
A solution to an linear equation cx + d = f is in the form x = a for some a, we call a the solution (a might not be unique). Rewrite your sentence: x = 8, 8 is unique. So how many solution does it have?
There are an infinite number of solutions to this equation, some of which are (9,0), (12,2), (15,4), (18,6), (21,8)
How about finding the solutions of the quadratic equation: x^2-14x+49 = 0
This equation describes all the points on the unit sphere. There is an infinite number of solutions. Some quick integer solutions would be (1,0,0) and (0,1,0) and (0,0,1) which are the one the axes.
No. Some have two solutions where as some have none.
Yes, that is often possible. It depends on the equation, of course - some equations have no solutions.
the Bratu's equation is a differential equation which is non-linear (such as, if we have some solutions for it, a linear combinaison of these solutions will not be everytime a solution). It's given by the equation y''+a*e^y=0 or d²y/dy² =-ae^y.
Start with the equation:x = 11 Then, to make the equation more complicated ("multi-step"), you can do different manipulations, always on both sides of the equation; for example: * Add some number to both sides * Multiply both sides by the same number * Square both sides, or apply some other function to both sides (note: this may introduce additional solutions, depending on the properties of the function applied)
It often helps to square both sides of the equation (or raise to some other power, such as to the power 3, if it's a cubic root).Please note that doing this may introduce additional solutions, which are not part of the original equation. When you square an equation (or raise it to some other power), you need to check whether any solutions you eventually get are also solutions of the original equation.
7
The roots of an equation means the solutions of an equation. Different methods have been developed for different kinds of equation. It is not possible to give an overview in one or two paragraphs, but in simpler cases, the same operation is done on both sides of the equation, with the aim of "isolating" the variable you are solving for, that is, having it alone on one side. In some complicated cases, no "explicit" solutions exist, and "numerical" solutions have to be used; this basically means using trial-and-error.
A solution to an linear equation cx + d = f is in the form x = a for some a, we call a the solution (a might not be unique). Rewrite your sentence: x = 8, 8 is unique. So how many solution does it have?
It is impossible to answer the question without some information about V or t or what the equation is meant to represent.