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Help and please explain part ) in detail! Thanks!

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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
$$x+y\neq\sqrt{x^2+y^2}?$$

Aug 29, 2018

#1
+971
+2

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.

Aug 29, 2018

#1
+971
+2

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.

GYanggg Aug 29, 2018
#2
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Thank you! This helped!

Guest Aug 29, 2018