Using euclid''s algorithm find the value of x & y, Mathematics

If d is the HCF of 30, 72, find the value of x & y satisfying d = 30x + 72y.

(Ans:5, -2 (Not unique)

Ans:    Using Euclid's algorithm, the HCF (30, 72)

72 = 30 × 2 + 12

30 = 12 × 2 + 6

12 = 6 × 2 + 0

HCF (30,72) = 6

6=30-12×2

6=30-(72-30×2)2

6=30-2×72+30×4

6=30×5+72×-2

∴ x = 5, y = -2

Also 6 = 30 × 5 + 72 (-2) + 30 × 72 - 30 × 72

Solve it, to get

x = 77, y = -32

Hence, x and y are not unique

Posted Date: 4/8/2013 1:06:39 AM | Location : United States







Related Discussions:- Using euclid''s algorithm find the value of x & y, Assignment Help, Ask Question on Using euclid''s algorithm find the value of x & y, Get Answer, Expert's Help, Using euclid''s algorithm find the value of x & y Discussions

Write discussion on Using euclid''s algorithm find the value of x & y
Your posts are moderated
Related Questions
Non Zero Sum Games Recently there was no satisfactory theory either to describe how people should play non-zero games or to explain how they actually play that game Nigel Ho

We know that 2 4 = 16 and also that 2 is referred to as the base, 4 as the index or power or the exponent. The same if expressed in terms of logarithms would be log 2

Give an example to illustrate how language incompetence can interfere with a child's ability to perform a task. While setting up a classification activity, a teacher gave the ch

(1) Show that the conclusion of Egroff's theorem can fail if the measure of the domain E is not finite. (2) Extend the Lusin's Theorem to the case when the measure of the domain E

Divide 6.8 × 10 5 by 2.0 × 10 2 . Write your answer in scientific notation? To divide numbers written in scienti?c notation and divide the ?rst numbers (6.8 ÷ 2.0 = 3.4); the

Evaluate following limits. Solution Here the first two parts are actually just the basic limits including inverse tangents and can easily be found by verifying the fol

L'Hospital's Rule Assume that we have one of the given cases, where a is any real number, infinity or negative infinity.  In these cases we have, Therefore, L'H

Liner Regression The calculations for our sample size n = 10 are described below. The linear regression model is y = a + bx Table: Distance x miles


together, pearl and harvey are going to visit their aunt on sunday. If Pearl visits their aunt every 6 days, while harvey every 8 days, on what day will they visit their aunt toget