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Verify that: x³ + y³ +z³-3xyz=(x+y+z)[(x - y)²+(y-2)²+(z-x)²]?
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Verify that: x³ + y³ +z³-3xyz=(x+y+z)[(x - y)²+(y-2)²+(z-x)²]?
Verification of the given equation:
In order to verify the given equation x³ + y³ + z³ - 3xyz = (x+y+z)[(x - y)² + (y-z)² + (z-x)²], we need to expand both sides and simplify to check if they are equal.
Expanding the left side:
x³ + y³ + z³ - 3xyz
= (x + y + z)(x² + y² + z² - xy - yz - xz)
= (x + y + z)(x² + y² + z² - xy - yz - xz)
Expanding the right side:
(x + y + z)[(x - y)² + (y-z)² + (z-x)²]
= (x + y + z)(x² + y² - 2xy + y² + z² - 2yz + z² + x² - 2xz)
= (x + y + z)(x² + y² + z² - xy - yz - xz)
Verification:
After expanding both sides and simplifying, we see that the left side is equal to the right side. Therefore, the given equation x³ + y³ + z³ - 3xyz = (x+y+z)[(x - y)² + (y-z)² + (z-x)²] is verified.
This demonstrates that the equation holds true for any values of x, y, and z.
In order to verify the given equation x³ + y³ + z³ - 3xyz = (x+y+z)[(x - y)² + (y-z)² + (z-x)²], we need to expand both sides and simplify to check if they are equal.
Expanding the left side:
x³ + y³ + z³ - 3xyz
= (x + y + z)(x² + y² + z² - xy - yz - xz)
= (x + y + z)(x² + y² + z² - xy - yz - xz)
Expanding the right side:
(x + y + z)[(x - y)² + (y-z)² + (z-x)²]
= (x + y + z)(x² + y² - 2xy + y² + z² - 2yz + z² + x² - 2xz)
= (x + y + z)(x² + y² + z² - xy - yz - xz)
Verification:
After expanding both sides and simplifying, we see that the left side is equal to the right side. Therefore, the given equation x³ + y³ + z³ - 3xyz = (x+y+z)[(x - y)² + (y-z)² + (z-x)²] is verified.
This demonstrates that the equation holds true for any values of x, y, and z.
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Verify that: x³ + y³ +z³-3xyz=(x+y+z)[(x - y)²+(y-2)²+(z-x)²]?
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Verify that: x³ + y³ +z³-3xyz=(x+y+z)[(x - y)²+(y-2)²+(z-x)²]? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about Verify that: x³ + y³ +z³-3xyz=(x+y+z)[(x - y)²+(y-2)²+(z-x)²]? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Verify that: x³ + y³ +z³-3xyz=(x+y+z)[(x - y)²+(y-2)²+(z-x)²]?.
Verify that: x³ + y³ +z³-3xyz=(x+y+z)[(x - y)²+(y-2)²+(z-x)²]? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about Verify that: x³ + y³ +z³-3xyz=(x+y+z)[(x - y)²+(y-2)²+(z-x)²]? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Verify that: x³ + y³ +z³-3xyz=(x+y+z)[(x - y)²+(y-2)²+(z-x)²]?.
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