Question

16x² + 9y² + 4z² = 24( x - y + z ) - 61 then find value of xy + 2z​

Answer 1

Answer with explanation:

$=16 x^2 + 9 y^2 + 4 z^2 = 24( x - y + z ) - 61\\\\=16 x^2-24 x+9+9y^2+24 y+16+4z^2-24 z+36+61-61=0\\\\\rightarrow (4x-3)^2+(3y+4)^2+(2z-6)^2=0$

This is Possible only when

  $4 x-3=0\\\\x=\frac{3}{4}\\\\3 y+4=0\\\\y=\frac{-4}{3}\\\\2 z-6=0\\\\z=\frac{6}{2}\\\\z=3$

We have to find the value of

   x y +2 z

$=\frac{3}{4} \times \frac{-4}{3}+2 \times 3\\\\= -1+6\\\\=5$