Express the HCF of 468 and 222 as 468x+222y to find x and y,where x,y are integers in two different ways.

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Express the HCF of 468 and 222 as 468x+222y to find x and y,where x,y are integers in two different ways.

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-9 and 19

19 and -9

213 and 449

449 and 213

answer is A.

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Detailed Solution

The HCF of 468 and 222.
Using, Euclid’s division algorithms,
222×2+24=468
24×9+6=222
6×4+0=24
HCF=6
Now, we have
6=222−24×9
⇒6=222−(468−222×2)×9
⇒6=222−9×468+222×18
⇒6=222×19−9×468
⇒6=468×(−9)+222×19. . . . (1)
HCF=468x+222y. . . . (2)
From the equation (1) and (2)
x=−9 and y=19
Here, we have written
6=xa+yb
⇒6=xa+yb+ab−ab
⇒6=a(x+b)+b(y−a)
⇒6=468(−9+222)+222(19−468)
⇒6=468×(213)+(−449)×222
⇒x=213 and y=−449

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