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Does a by b plus b by c plus c by a equals 3 imply that abc is the cube of an integer when a b c are integers?
No. Here is a proof by counterexample that it does not.
Given ab + bc + ca = 3:
Assume toward a contradiction that abc is a cube. Then a = b = c.
Without loss of generality, let a = 2, b = 2, and c = 2.
Then ab = 4, bc = 4, and ca = 4.
ab + bc + ca = 4 + 4 + 4 = 12.
Therefore, 12 = 3, which is false, and so the original statement is false.
What else can I help you with?
Is 11025 a perfect cube?
No, 11025 is not a perfect cube. A perfect cube is an integer that can be expressed as the cube of another integer. The cube root of 11025 is approximately 22.2, which is not an integer, indicating that 11025 cannot be written as ( n^3 ) for any integer ( n ).
The square root of a perfect square and the cube root of a perfect cube is?
an integer
What is the smallest integer where the integer before it is a perfect square and the integer after it is a perfect cube?
The integer is 26
How is 784 a perfect cube?
The number 784 is not a perfect cube. A perfect cube is defined as a number that can be expressed as the cube of an integer (i.e., (n^3) for some integer (n)). The cube root of 784 is approximately 9.24, which is not an integer, indicating that 784 cannot be represented as a whole number cubed.
What is the least positive integer x for which 12x is the cube of an integer?
2
Is 11025 a perfect cube?
No, 11025 is not a perfect cube. A perfect cube is an integer that can be expressed as the cube of another integer. The cube root of 11025 is approximately 22.2, which is not an integer, indicating that 11025 cannot be written as ( n^3 ) for any integer ( n ).
The square root of a perfect square and the cube root of a perfect cube is?
an integer
What is the smallest integer where the integer before it is a perfect square and the integer after it is a perfect cube?
The integer is 26
Is 77 a cube number?
If by cube you mean perfect cube (a cube of an integer), then no, and the nearest perfect cube is 81.
How is 784 a perfect cube?
The number 784 is not a perfect cube. A perfect cube is defined as a number that can be expressed as the cube of an integer (i.e., (n^3) for some integer (n)). The cube root of 784 is approximately 9.24, which is not an integer, indicating that 784 cannot be represented as a whole number cubed.
What is the least positive integer x for which 12x is the cube of an integer?
2
Why are perfect square and cube perfect?
Because they are square/cube of an integer.
What is the difference between a cube and a perfect cube?
A cube is any number multiplied by itself three times, eg 2 cubed = 2³ = 2×2×2 = 8; 1.5³ = 1.5×1.5×1.5 = 3.375 A perfect cube is an integer (whole number) that is the cube of an integer, eg 8 is a perfect cube as it is 2 cubed, but 9 is not a perfect cube as 9 = 2.08008382...³
What is the smallest positive integer e such that the cube root of 600e is an integer?
45
What is the least positive integer x for which 594x is the cube of an integer?
x = 484
What is the smallest possible value of k if k is a perfect cube?
The smallest possible value of ( k ) if ( k ) is a perfect cube is ( 1 ), since ( 1^3 = 1 ). Perfect cubes are formed by multiplying integers by themselves three times, and the smallest integer, which is ( 1 ), yields the smallest perfect cube. Therefore, ( k = 1 ) is the answer.
What is the operations of integers?
There is no "operation of integers".There are some operations that can be defined for single integers such as: additive inverse (= negative), multiplicative inverse (= reciprocal, not defined for 0), absolute value, square, cube, nth power, square root (if non-negative), cube root and so on.Then there are operations that can be defined for two integers, such as sum, difference, absolute difference, product, quotient (if the second integer is not 0), exponent, logarithm of one to the other as base (if they are both positive), and so on.
