Question

$if {x}^{3} + {y}^{3} + {z}^{3} = 3xyz.$
Then show that x=y=z(with proof).

Answer 1

◢GIVEN

=> x³ + y³ + z³ = 3xyz

◢SHOW THAT

=> x = y = z

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● IT IS POSSIBLE OR TRUTH ONLY FOR 3 VALUE OF x, y and z

● AND THE VALUE OF x, y and z = 0, -1 and 1

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[1]

◢FOR "0"

=> x³ + y³ + z³ = 3xyz

● PLUG THE VALUE => x = y = z = 0

=> 0³ + 0³ + 0³ = 3×0×0×0

=> 0 = 0 ________[◢PROVED]

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[2]

◢FOR "-1"

=> -1³ + -1³ + -1³ = 3(-1)(-1)(-1)

=> -1 -1 -1 = -3

=> -3 = -3 ____________[◢PROVED]

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[3]

◢FOR "1"

=> 1³ + 1³ + 1³ = 3×1×1×1

=> 1 + 1 + 1 = 3

=> 3 = 3 ______________[◢PROVED]

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◢THEN,

$YOUR \: \: STATEMENT \: \: TRUTH \: \: \: OR \: \: \\ POSSIBLE \: \: ONLY \: \:FOR THREE (3) \: \: VALUE \: \: OF \\ \: \: x \: \: y \: \: AND \: \: z \: \: THESE \: \: VALUES \: ARE \: \:$

=> x = y = z = 0

=> x = y = z = -1

=> x = y = z = 1
___________________[◢PROVED]

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☆$BE \: \: BRAINLY$☆