Question

Find the value of x + y + z if x² + y² + 4z² + 12z +29 - 4x - 8y = 0.​

Answer 1

Answer:

SOLUTION FOR THE QUESTIONIS -

X²+Y²+Z²_4X_8Y€6Z+29=0

(X²_4X+4)+(Y²_ 8Y+16) +(Z²_12Z+24)=0

(X_2)²+(Y_4)²+(Z_12)²=0

EACH TERM HERE IS POSITIVE SO EACH TERM MUST BE ZERO TO GET THE SUM AS ZERO SO,X_2=0,Y_4=0,Z_12=0

WE GET X=2 Y=4 Z=12

Answer 2

Answer:

$\frac{9}{2}$

Step-by-step explanation:

x² + y² + 4z² + 12z +29 - 4x - 8y = 0.

or, x²-4x+4+y²-8y+16+z²+12z+9=0

or, (x-2)²+(y-4)²+(2z-3)²=0

Thus, x=2, y=4, z=$\frac{-3}{2}$.

Value of x+y+z= 2+4$\frac{-3}{2}$

=$\frac{9}{2}$