find out the value of $\dfrac {x^2}{9}+\dfrac {y^2}{25}+\dfrac {z^2}{16}$

Question

If $(x-3)^2+(y-5)^2+(z-4)^2=0$,then find out the value of $$\dfrac {x^2}{9}+\dfrac {y^2}{25}+\dfrac {z^2}{16}$$

just give hint to start solution.

Answer 1

HINT: Assuming real solutions, there is only one possibility for values of $x, y$ and $z$. Then put in the corresponding values in the 2nd expression. If they are complex then there are infinite values.

Answer 2

Hint: What values does the function $x^2$ acquire(positive/negarive)? What is the solution of the equation $x^2=0$?

Can you find the solution of the equation $x^2+y^2=0$?

Now, what can you say about the equation $(x-3)^2+(y-5)^2+(z-4)^2=0 $? Can you find the values of $x,y,z?$

Answer 3

Hint: $(x-3)^3\geq0,(y-5)^2\geq0,(z-4)^2\geq0$.