Topic Details (Notes format)

How to Solve Simple Diophantine Equations with Two Unknowns

Subject: Mathematics

Book: Maths Mastery

A Diophantine equation restricts solutions to integers. A typical linear form is Ax + By = C. For instance, 4x + 6y= 14 can be tackled by factoring out gcd(4,6)=2, rewriting as 2(2x+3y)=14, so 2x+3y=7. Then find integer solutions systematically. Another approach is the Extended Euclidean Algorithm. These equations are fundamental in partitioning tasks, cryptographic key generation, or advanced number theory. Mastering them ensures a strong integer-based solution approach for logic puzzles or real-world quantity allocations that must remain whole.

Practice Questions

A sphere has a radius of 7 cm. What is its volume?

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If sin(x) = 3/5 and x is in the first quadrant, what is cos(x)?

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The sum of the squares of two consecutive integers is 145. What are the integers?

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If x² - 9x + 18 = 0, what are the roots of the equation?

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What is the area of an equilateral triangle with side length 10 cm?

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A sum triples in 20 years at simple interest. What is the rate of interest per annum?

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If the cost price of an item is Rs. 400 and the selling price is Rs. 500, what is the profit percentage?

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If a cylinder has a radius of 7 cm and height of 10 cm, what is its volume?

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If a + b = 10 and ab = 21, what is the value of a^2 + b^2?

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If x:y = 2:3 and z:y = 4:3, what is x:z?

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