Class 9 Exam > Class 9 Questions > If x = 2^(1⁄3)+2^(2⁄3), show that x^3-6x=6.?
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If x = 2^(1⁄3)+2^(2⁄3), show that x^3-6x=6.?
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If x = 2^(1⁄3)+2^(2⁄3), show that x^3-6x=6.?
Proof that x^3 - 6x = 6
- Let's start by calculating x^3:
Calculate x^3:
x = 2^(1/3) + 2^(2/3)
x^3 = (2^(1/3) + 2^(2/3))^3
= 2^(1) + 3*(2^(1/3))*(2^(2/3)) + 3*(2^(1/3))*(2^(2/3)) + 2^(2)
= 2 + 3*2 + 3*2 + 4
= 2 + 6 + 6 + 4
= 18
- Now, let's calculate 6x:
Calculate 6x:
6x = 6(2^(1/3) + 2^(2/3))
= 6*2^(1/3) + 6*2^(2/3)
= 6*2^(1/3) + 12*2^(1/3)
= 18*2^(1/3)
- Finally, let's subtract 6x from x^3 and show that it equals 6:
Subtract 6x from x^3:
x^3 - 6x = 18 - 18
= 0
Therefore, x^3 - 6x = 0, not 6.
- Let's start by calculating x^3:
Calculate x^3:
x = 2^(1/3) + 2^(2/3)
x^3 = (2^(1/3) + 2^(2/3))^3
= 2^(1) + 3*(2^(1/3))*(2^(2/3)) + 3*(2^(1/3))*(2^(2/3)) + 2^(2)
= 2 + 3*2 + 3*2 + 4
= 2 + 6 + 6 + 4
= 18
- Now, let's calculate 6x:
Calculate 6x:
6x = 6(2^(1/3) + 2^(2/3))
= 6*2^(1/3) + 6*2^(2/3)
= 6*2^(1/3) + 12*2^(1/3)
= 18*2^(1/3)
- Finally, let's subtract 6x from x^3 and show that it equals 6:
Subtract 6x from x^3:
x^3 - 6x = 18 - 18
= 0
Therefore, x^3 - 6x = 0, not 6.
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If x = 2^(1⁄3)+2^(2⁄3), show that x^3-6x=6.?
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If x = 2^(1⁄3)+2^(2⁄3), show that x^3-6x=6.? 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 If x = 2^(1⁄3)+2^(2⁄3), show that x^3-6x=6.? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If x = 2^(1⁄3)+2^(2⁄3), show that x^3-6x=6.?.
If x = 2^(1⁄3)+2^(2⁄3), show that x^3-6x=6.? 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 If x = 2^(1⁄3)+2^(2⁄3), show that x^3-6x=6.? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If x = 2^(1⁄3)+2^(2⁄3), show that x^3-6x=6.?.
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