Question

Solve the above question.

•it should be neat & clean ☺
•wrong or unnecessary solutions will be reported !!

Answer 1

Heya User,

--> Let's learn our childhood drawing steps :p
^_^ Tracing other's drawings that is :p

--> We use Euclid's division algorithm for finding the HCF { which is sooooo length }

--> 237 = 81 * 2 + 75
-->  81  = 75 * 1 + 6
-->  75  = 6 * 12 + 3
-->  6  = 3 * 2

Since, 3 remains at last, we get the GCD as ---> '3'

Now, our favorite part --> " Tracing back our steps "
--> 3 = 75 - 6 ( 12 )
=> 3 = 75 - ( 81 - 75 )( 12 ) = 75 ( 13 ) - 81 ( 12 )
=> 3 = [ 237 - 81(2) ] ( 13 ) - 81 ( 12 )
=> 3 = 237 ( 13 ) - 81 ( 26 ) - 81 ( 12 )
=> 3 = 237 ( 13 ) - 81 ( 38 )
=> 3 = 81 ( - 38 ) + 237 ( 13 )

Comparing this with GCD ( 81 , 237 ) = 81x + 237y :->

We Get --> 
---> x = ( -38 ) || y = 13   ... We got it .. Yay !

=_= In case uh have sth to ask.. Just comment below ^_^

Answer 2

By Euclid's Division Algorithm,

237=81(2)+(75)

81=75(1) + (6)

75=6(12)+(3)

6=3(2)+(0)

Hcf =3

 

Expressing it in the form of 237x+81y=HCF

3=75-6(12)  { From 2nd last step}

3=75-(81-75)(12)  {Substituting}

3=75-(81*12-75*12)

3=75-81*12+75*12

3=75(13)-81(12)

3=(237-81*2)(13)-81(12)

3=237(13)-81(38)

3=237(13)+81(-38)  {we need an expression in the form 237x + 81y }

Therefore, x =13 , y =- 38