verify that X3 +Y3+Z3-3XYZ=1/2 (X+Y+Z ) [(X+Y)2+(Y-Z)2+(Z-X)2]
Answers
Answered by
22
First We take R.H.S & use the Formula [( a-b)²= a²+b²-2ab] & simplify it then R.H.S becomes equal to L.H.S
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)]
================================================================
Hope this will help you....
Please mark me as brainliest,Thank you and follow me.
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)]
================================================================
Hope this will help you....
Please mark me as brainliest,Thank you and follow me.
Similar questions