Question

please solve it and full solution

Answer 1

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By Euclid's Division Lemma

=> HCF(275,200)

=> 275 = 200 x 1 + 75 --------(3)

=> 200 = 75 x 2 + 50 ------(2)

=> 75 = 50 x 1 + 25 -------(1)

=> 50 = 25 x 2 + 0

=> HCF(275,200) = 25

For Expression part, using (1)

=> 75 = 50 x 1 + 25

=> 25 = 75 - (50 x 1)

Substituting 50 in (2) in above equation

=> 25 = 75 - [(200) - (75 x 2)]

=> 25 = 75 - 200 + 75(2)

=> 25 = 75(3) - 200

Now, final step , substituting 75 from (3) in above equation

=> 25 = [ 275 - (200 x 1)]3 - 200(2)

=> 25 = 275(3) - 200(3) - 200(2)

=> 25 = 275(3) - 200(5)

=> 25 = 275(3) + 200(-5)

=> 25 = 275x + 200y

where x = 3 and y = -5

Hence Proved

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Hope this helps ✌️