The problem asks us to determine what we know about the solutions to the equation $xyz = 0$. Here, $x$, $y$, and $z$ are three numbers.

AlgebraEquationsZero Product PropertyVariables
2025/6/4

1. Problem Description

The problem asks us to determine what we know about the solutions to the equation xyz=0xyz = 0. Here, xx, yy, and zz are three numbers.

2. Solution Steps

For the product of three numbers to be equal to zero, at least one of the numbers must be zero. That is, if xyz=0xyz = 0, then either x=0x=0 or y=0y=0 or z=0z=0. It is also possible that two or three of them are zero.

3. Final Answer

At least one of the numbers xx, yy, or zz must be equal to zero.

Related problems in "Algebra"

The problem is to analyze the equation $x^3 + y^3 = 3y$. We are asked to solve this equation. Howeve...

Cubic EquationsEquation SolvingVariables
2025/6/6

We are given the equation $12x + d = 134$ and the value $x = 8$. We need to find the value of $d$.

Linear EquationsSolving EquationsSubstitution
2025/6/5

We are given a system of two linear equations with two variables, $x$ and $y$: $7x - 6y = 30$ $2x + ...

Linear EquationsSystem of EquationsElimination Method
2025/6/5

We are given two equations: 1. The cost of 1 rugby ball and 1 netball is $£11$.

Systems of EquationsLinear EquationsWord Problem
2025/6/5

The problem asks to solve a system of two linear equations using a given diagram: $y - 2x = 8$ $2x +...

Linear EquationsSystems of EquationsGraphical SolutionsIntersection of Lines
2025/6/5

We are asked to solve the absolute value equation $|5x + 4| + 10 = 2$ for $x$.

Absolute Value EquationsEquation Solving
2025/6/5

The problem is to solve the equation $\frac{x}{6x-36} - 9 = \frac{1}{x-6}$ for $x$.

EquationsRational EquationsSolving EquationsAlgebraic ManipulationNo Solution
2025/6/5

Solve the equation $\frac{2}{3}x - \frac{5}{6} = \frac{3}{4}$ for $x$.

Linear EquationsFractionsSolving Equations
2025/6/5

The problem is to solve the following equation for $x$: $\frac{42}{43}x - \frac{25}{26} = \frac{33}{...

Linear EquationsFractional EquationsSolving EquationsArithmetic OperationsFractions
2025/6/5

The problem is to solve the linear equation $2(x - 2) - (x - 1) = 2x - 2$ for $x$.

Linear EquationsEquation SolvingAlgebraic Manipulation
2025/6/5