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How many solutions are there to the equation
x₁ + x₂ + x₃ + x₄ = 17,
where x₁, x₂, x₃, x₄ are non-negative integers?
x₁ + x₂ + x₃ + x₄ = 17,
where x₁, x₂, x₃, x₄ are non-negative integers?
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How many solutions are there to the equation x₁ + x₂ + x₃ + x₄ = 17, w...
Introduction
The given equation is x₁ x₂ x₃ x₄ = 17, where x₁, x₂, x₃, x₄ are non-negative integers. We need to find the number of solutions for this equation.
Prime Factorization of 17
The prime factorization of 17 is 17 = 1 * 17. As 17 is a prime number, it has only two factors, 1 and 17.
Counting Solutions
We can count the number of solutions of the equation x₁ x₂ x₃ x₄ = 17 by considering all possible combinations of factors of 17. Since 17 has only two factors, there are only two ways to express 17 as a product of four non-negative integers:
1. x₁ = 1, x₂ = 1, x₃ = 1, x₄ = 17: There is only one solution for this case, which is (1, 1, 1, 17).
2. x₁ = 1, x₂ = 17, x₃ = 1, x₄ = 1: There is only one solution for this case, which is (1, 17, 1, 1).
Therefore, the total number of solutions for the equation x₁ x₂ x₃ x₄ = 17 is 2.
Conclusion
We have found that there are only two solutions for the equation x₁ x₂ x₃ x₄ = 17, which are (1, 1, 1, 17) and (1, 17, 1, 1).
The given equation is x₁ x₂ x₃ x₄ = 17, where x₁, x₂, x₃, x₄ are non-negative integers. We need to find the number of solutions for this equation.
Prime Factorization of 17
The prime factorization of 17 is 17 = 1 * 17. As 17 is a prime number, it has only two factors, 1 and 17.
Counting Solutions
We can count the number of solutions of the equation x₁ x₂ x₃ x₄ = 17 by considering all possible combinations of factors of 17. Since 17 has only two factors, there are only two ways to express 17 as a product of four non-negative integers:
1. x₁ = 1, x₂ = 1, x₃ = 1, x₄ = 17: There is only one solution for this case, which is (1, 1, 1, 17).
2. x₁ = 1, x₂ = 17, x₃ = 1, x₄ = 1: There is only one solution for this case, which is (1, 17, 1, 1).
Therefore, the total number of solutions for the equation x₁ x₂ x₃ x₄ = 17 is 2.
Conclusion
We have found that there are only two solutions for the equation x₁ x₂ x₃ x₄ = 17, which are (1, 1, 1, 17) and (1, 17, 1, 1).
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How many solutions are there to the equation x₁ + x₂ + x₃ + x₄ = 17, where x₁, x₂, x₃, x₄ are non-negative integers?
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How many solutions are there to the equation x₁ + x₂ + x₃ + x₄ = 17, where x₁, x₂, x₃, x₄ are non-negative integers? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about How many solutions are there to the equation x₁ + x₂ + x₃ + x₄ = 17, where x₁, x₂, x₃, x₄ are non-negative integers? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for How many solutions are there to the equation x₁ + x₂ + x₃ + x₄ = 17, where x₁, x₂, x₃, x₄ are non-negative integers?.
How many solutions are there to the equation x₁ + x₂ + x₃ + x₄ = 17, where x₁, x₂, x₃, x₄ are non-negative integers? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about How many solutions are there to the equation x₁ + x₂ + x₃ + x₄ = 17, where x₁, x₂, x₃, x₄ are non-negative integers? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for How many solutions are there to the equation x₁ + x₂ + x₃ + x₄ = 17, where x₁, x₂, x₃, x₄ are non-negative integers?.
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