If for all \(\displaystyle a\) we have \(\displaystyle a^2\ge 0\) then \(\displaystyle (x-1)^2\ge 0~\&~(y-1)^2\ge 0\).WannaBe said:Prove that for any two numbers x,y we have [(x^2 + y^2)/2] >= x + y - 1
Solution)
For any number a we have have a^2 > 0. So,
(x-1)^2 + (y-1)^2 >= 0
And if we solve this we get the solution.
A two variable inequality is an inequality that contains two variables, typically represented by x and y. This means that the values of both variables can vary and the inequality will still hold true.
To graph a two variable inequality, first plot the boundary line of the inequality, which is usually a straight line. Then, depending on whether the inequality is greater than or less than, shade the region above or below the boundary line. The shaded region represents all the possible solutions to the inequality.
A one variable inequality only contains one variable, while a two variable inequality contains two variables. This means that the solutions to a one variable inequality are represented on a number line, while the solutions to a two variable inequality are represented on a coordinate plane.
To solve a two variable inequality, first graph the inequality and find the shaded region. Then, pick a point within the shaded region and substitute its coordinates into the inequality. If the inequality is true, then all points in the shaded region are solutions. If the inequality is false, then all points outside the shaded region are solutions.
In science, it is common to have multiple variables that affect the outcome of an experiment or study. Understanding two variable inequalities allows scientists to accurately represent and analyze these complex relationships between variables. It also helps in making predictions and identifying patterns in data sets.