Question

if x+y+z=5 and xy +yz+zx=10 then prove that x^3 +y^3+z^3-3xyz= -25

Answer 1

Answer:

Step-by-step explanation:

I hope it will be helpful.

Answer 2

x+y+z=5. xy+yz+zx=10

$to \: prove \: - x {}^{3} + {y}^{3} + {z}^{3} - 3xyz = - 25$

${x}^{3} + {y}^{3} + {z}^{3} - 3 \times yz = (x + y + z )( {x}^{2} + {y}^{2} + {z}^{2} - xy - yz - zx)$

$( {x + y + z}^{2} ) = {(5)}^{2}$

${x}^{2} + {y}^{2} + {z}^{2} + 2(xy + yz + zx) = 25$

${x}^{2} + {y}^{2} + {z}^{2} + 20 = 25$

${x}^{2} + {y}^{2} + {z}^{2} = 5$

$(x + y + z)( {x}^{2} + {y}^{2} + {z}^{2} - xy - yz - zx)$

$5(5 - (xy -yz -zx))$

$5(5 - 10)$

$= - 25$

I hope this will help you friend