a) Compute \(x+y\) and \(\sqrt{x^2+y^2}\) when \(x+5\) and \( y=12\)
b) When is
\(x+y=\sqrt{x^2+y^2}?\)
When is
\(x+y\neq\sqrt{x^2+y^2}?\)
+983 a)
You just plug in the values, and evaluate the expression.
b)
\(x+y=\sqrt{x^2+y^2}\\ (x+y)^2=x^2+y^2\\ x^2+2xy+y^2=x^2+y^2\\ 2xy=0\)
Therefore, either x, y, or both variables have to be 0 for the expression to be equal.
This works in reverse. If \(x+y\ne\sqrt{x^2+y^2}\), then \(2xy\ne0\).
I hope this helped,
Gavin.
+983 a)
You just plug in the values, and evaluate the expression.
b)
\(x+y=\sqrt{x^2+y^2}\\ (x+y)^2=x^2+y^2\\ x^2+2xy+y^2=x^2+y^2\\ 2xy=0\)
Therefore, either x, y, or both variables have to be 0 for the expression to be equal.
This works in reverse. If \(x+y\ne\sqrt{x^2+y^2}\), then \(2xy\ne0\).
I hope this helped,
Gavin.
