X 2 Y 2 1 3 X 2y 3 SemajkruwSantana from semajkruwsantana.blogspot.com
Introduction
In mathematics, an equation is a statement that contains an equal sign and can be solved to find the value of the variable. The equation x2y2+1=3x2y3 is an algebraic equation that contains two variables x and y. In this article, we will explain how to solve this equation step-by-step.
Understanding the Equation
The equation x2y2+1=3x2y3 can be simplified by rewriting it as x2y2-3x2y3+1=0. This equation is a polynomial equation of degree 3 in y and degree 2 in x. It is not a linear equation, which means that it does not have a straight-line graph.
Step-by-Step Solution
To solve the equation x2y2+1=3x2y3, we need to follow these steps:
Step 1: Simplify the Equation
As mentioned earlier, we can simplify the equation by rewriting it as x2y2-3x2y3+1=0.
Step 2: Factor Out x2y2
We can factor out x2y2 from the equation to get x2y2(1-3y)+1=0.
Step 3: Solve for y
We can now solve for y by setting the expression in the parentheses equal to zero. Thus, we have 1-3y=0, which gives us y=1/3.
Step 4: Substitute y=1/3 into the Equation
Now that we have the value of y, we can substitute it into the original equation to find the value of x. Thus, we have x2(1/3)2+1=3x2(1/3)3, which simplifies to x2/9+1=1/3x2.
Step 5: Solve for x
We can now solve for x by multiplying both sides of the equation by 9x2. This gives us x2+9x2=3, which simplifies to 10x2=3. Thus, we have x=±√(3/10).
Conclusion
In conclusion, the equation x2y2+1=3x2y3 is an algebraic equation that can be solved using the steps outlined above. By simplifying the equation, factoring out x2y2, solving for y, substituting y=1/3 into the equation, and solving for x, we were able to find the values of x and y. It is important to note that there may be more than one solution to this equation, and it is always a good idea to check your answer by substituting it back into the original equation.
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