90) If x 2 + 4 y 2 + 9 z 2 - 2 x - 12 y + 10 = 0 then the value of x + y + z is
(1) 2.5
(2) 2.4
(3) 2.3
(4) 2.0

Dear Student,

x2+4y2+9z2-2x-12y+10=0x2-2x+1+4y2-12y+9+9z2=0x2-2x+12+2y2-12y+32+3z2=0x-12+2y-32+3z2=0
As we know that square of any number is positive. Sum of three positive numbers is zero only if all the three numbers are zero.
x-1=0, 2y-3=0, 3z=0x=1, y=32, z=0x+y+z=1+32=52=2.5
Regards,

  • 4
X+ 4Y+ 9Z- 2X- 12Y+10 = 0
(X-1)2+(2Y-3)2+(3Z)2=0
AS ALL VALUE ARE NON-NEGATIVE BECAUSE OF SQUARE, therefore ADDITION OF NON-NEGATIVE NO. IS ZERO WHEN ALL THE VALUES ARE ZERO.
SO,  X=1 ,Y=3/2 & Z=0
HENCE X+Y+Z= 1+3/2+0=5/2=2.5
  • 0
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