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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?
Wiki User
∙ 12y ago
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.
Wiki User
∙ 12y ago
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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
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
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.
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 least positive integer x for which 594x is the cube of an integer?
x = 484
What is the smallest positive integer e such that the cube root of 600e is an integer?
45
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.
To get perfect cube?
You multiply an integer by itself twice or multiply 1 by an integer three times.
What is the cube root of 700 to the nearest integer?
9
Is the cube root of 5 irrational?
Yes it is. There is no fraction which, when cubed, equates to 5. Consider n = p/q where p and q are integers expressed in lowest terms (they are relatively prime). If n3 = 5, then p3 / q3 = 5. This equates to an integer if and only if q3 = 1 meaning q = 1 or if p3 is divisible by q3. The latter is impossible since p and q are relatively prime. Thus, for n to be the cube root of 5 and be rational, it must be an integer. No integer cubes to 5 (1, 8, ...). Thus, the cube root of 5 is irrational.
