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Grade: 12

                        

IF d IS H.C.F OF 56 AND 72 FIND x,y SATISFYING d=56x+72y. Also show that x and y are not unique

6 years ago

Answers : (2)

Pallavi Das
17 Points
							According to Euclid`s algorithm,
   a=bq+r
so 72=56*1+16  ......(1)
     56=16*3+8     .....(2)
     16=8*2+0
H.C.F (56,72)= 8

Now 8=56-16*3   ......(2)
        8=56- (72-56*1)*3   .....(1)
        8=56- (72-56)*3
        8=56-3(72-56)
        8=56-72*3 +56*3
        8=56(1+3) +72(-3)
        8=56*4 +72(-3)
    Taking x=4 and y=-3 
          8=56x+72y
 Also x and y not equal to 1(Proved).
						
6 years ago
Pradhuman
11 Points
							According to Euclid division Lemma72=56*1+1656=16*3+816=8*2+0.......  Therefore 8 is the HCF. Now,,,, 8=56-(16*3)..... In this step we have expressed 8 in form of 56 and 16,  we have to express it in the form of 56 and 72. So,            Now by splliting 16  we get,.       8=56-(72-56*1)(3)      8 =56-72*3+56*3.......   As we have another 56 we group them    8 =56*4+72(-3).  Hence X and Y are 4,3 respectively .. Therefore X and Y are not equal
						
2 years ago
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