Question

If x+y+ z = 8 and xy +yz+zx = 20 find the value of x^3 +y^3 +z^3 -3xyz

Answer 1

Answer:

492

Step-by-step explanation:

using this identity, we can find the solution to your question

a³ + b³ + c³ – 3abc = (a + b + c)(a² + b² + c² – ab – bc – ca)

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

RHS = (x+y+z)(x²+y²+z²-xy-yz-xz)

          (x+y+z){x²+y²+z²-(xy+yz+xz)}      (i have taken -ve symbol (-) outside the bracket)

          substitute the values

         (8)(x+y+z)²-(20)

        (8)(8)²-20

         (8×64)-20

         512-20

         492//

therefore,

x³+y+z³-3xyz = 492

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