12. Verify that x + y + z- 3xyz = 1/2
(x + y + x) [(x – y) + (y – 3) + (z – x)]​

1 thought on “12. Verify that x + y + z- 3xyz = 1/2<br />(x + y + x) [(x – y) + (y – 3) + (z – x)]​”

1. Answer:

   ♚ ｈｅ ♬

   Step-by-step explanation:

   .. & [( -)²= ²+²-] & .. ..

   R.H.S

   ⇒ 1/2×(x + y + z) (x²+ y²-2xy +y²+ z²-2yz+x²+z²-2xz)

   [( a-b)²= a²+b²-2ab]

   ⇒ 1/2×(x + y + z) (2x²+ 2y²+2z²-2xy -2yz-2xz)

   ⇒ 1/2×(x + y + z) 2(x² + y²+ z² – xy – yz – xz)

   =(x + y + z) (x² + y²+ z² – xy – yz – xz)

   = x³+y³+z³-3xyz

   = L.H.S

   We know that,

   [x³+ y³ + z³– 3xyz = (x + y + z)(x²+ y² + z² – xy – yz – xz)]

   L.H.S = R.H.S

   [x³+ y³ + z³– 3xyz = (x + y + z)(x²+ y² + z² – xy – yz – xz)]

   ================================================================

   •?((¯°·._.• •._.·°¯((?•

   Reply