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Without actually calculating the cubes,find the value of (12)cube+(7)cube+(5)cube?
Verified Answer
Without actually calculating the cubes,find the value of (12)cube+(7)c...
We know that x^3 + y^3+ z^3 - 3xyz = (x + y + z) (x^2 + y^2 + z^2 - xy - yz - zx)
So, x^3 + y^3 + z^3 = 3xyz + (x + y + z) (x^2 + y^2 + z^2 - xy - yz - zx)
Putting x = -12, y = 7 , z = 5
(-12)^3 + (7)^3 + (5)^3
= 3 (-12) (7)(5) + (- 12 + 7 + 5) ((-12)^2 + (7)^2 + (5)2- (-12)(7) - (7)(5) - (5)(-12) )
= 3 (-12) (7)(5) + (0) ((-12)^2 + (7)^2+ (5)^2- (-12)(7) - (7)(5) - (5)(-12)
= 3 (-12) (7)(5)
= -1260
This question is part of UPSC exam. View all Class 9 courses
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Without actually calculating the cubes,find the value of (12)cube+(7)c...
Breaking down the problem:
To find the value of (12)³ + (7)³ + (5)³ without actually calculating the cubes, we can use a property of numbers involving their remainders when divided by 9.
Property of cubes modulo 9:
- When a number is divided by 9, the remainder of its cube is the same as the remainder of the number itself.
- For example, (12)³ ≡ 12 (mod 9), (7)³ ≡ 7 (mod 9), and (5)³ ≡ 5 (mod 9).
Applying the property:
- Now, we can calculate the remainders of 12, 7, and 5 when divided by 9.
- 12 ÷ 9 has a remainder of 3, 7 ÷ 9 has a remainder of 7, and 5 ÷ 9 has a remainder of 5.
Calculating the sum:
- Using the remainders, we can rewrite the expression as 3 + 7 + 5.
- Adding these values together, we get 15.
Therefore, the value of (12)³ + (7)³ + (5)³ is equal to 15 without actually calculating the cubes. This method saves time and simplifies the calculation process.
To find the value of (12)³ + (7)³ + (5)³ without actually calculating the cubes, we can use a property of numbers involving their remainders when divided by 9.
Property of cubes modulo 9:
- When a number is divided by 9, the remainder of its cube is the same as the remainder of the number itself.
- For example, (12)³ ≡ 12 (mod 9), (7)³ ≡ 7 (mod 9), and (5)³ ≡ 5 (mod 9).
Applying the property:
- Now, we can calculate the remainders of 12, 7, and 5 when divided by 9.
- 12 ÷ 9 has a remainder of 3, 7 ÷ 9 has a remainder of 7, and 5 ÷ 9 has a remainder of 5.
Calculating the sum:
- Using the remainders, we can rewrite the expression as 3 + 7 + 5.
- Adding these values together, we get 15.
Therefore, the value of (12)³ + (7)³ + (5)³ is equal to 15 without actually calculating the cubes. This method saves time and simplifies the calculation process.
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Without actually calculating the cubes,find the value of (12)cube+(7)cube+(5)cube?
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Without actually calculating the cubes,find the value of (12)cube+(7)cube+(5)cube? 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 Without actually calculating the cubes,find the value of (12)cube+(7)cube+(5)cube? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Without actually calculating the cubes,find the value of (12)cube+(7)cube+(5)cube?.
Without actually calculating the cubes,find the value of (12)cube+(7)cube+(5)cube? 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 Without actually calculating the cubes,find the value of (12)cube+(7)cube+(5)cube? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Without actually calculating the cubes,find the value of (12)cube+(7)cube+(5)cube?.
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