Question

There are infinitely How many pairs of numbers of which the sum of their cube roots is zero give two of these pairs

Answer 1

Infinite pairs of numbers

1 and -1

8 and -8

Explanation:

Let x³ and y³ be any two real numbers. If the sum of their cube roots is zero, then the following must be true:

`\sqrt[3]{x^3}+ \sqrt[3]{y^3}=0\\ \sqrt[3]{x^3}=- \sqrt[3]{y^3}\\x=-y`

Therefore, any pair of numbers with same absolute value but different signs fit the description, which means that there are infinite pairs of possible numbers.

Examples: 1 and -1; 8 and -8; 27 and -27.