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anemone
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Find the real solutions for ##\sqrt{z-y^2-6x-26}+x^2+6y+z-8=0##.
Here is my solution;anemone said:Find the real solutions for ##\sqrt{z-y^2-6x-26}+x^2+6y+z-8=0##.
A 3-variable equation is an equation that contains three variables, typically represented by x, y, and z. These equations involve finding the values of the variables that satisfy the equation and can be solved using algebraic methods.
To solve a 3-variable equation with real solutions, you need to isolate one variable on one side of the equation and then use substitution to solve for the other two variables. This process may involve using algebraic manipulations such as factoring, combining like terms, and using the quadratic formula.
Real solutions are values of the variables that satisfy the given equation and are represented by real numbers. In other words, when you plug in the values of the variables into the equation, the equation will be true.
Finding real solutions in a 3-variable equation is important because it allows us to understand the relationship between the variables and solve real-world problems. Real solutions represent possible solutions in the context of the problem and can help us make informed decisions.
Step 1: Isolate the square root term by subtracting x^2, 6y, and z from both sides of the equation.Step 2: Square both sides of the equation to eliminate the square root.Step 3: Use algebraic manipulations to get all the variables on one side of the equation and the constant term on the other side.Step 4: Use the quadratic formula to solve for one variable in terms of the other two variables.Step 5: Substitute the value of the solved variable into the original equation to get a 2-variable equation.Step 6: Solve the 2-variable equation using substitution or elimination.Step 7: Substitute the values of the solved variables into the original equation to get the real solutions.