Question

find the HCF of 81 and 237 and express it as a linear combination of 81 and 237.

Answer 1

75-(81-75*1)*12
75-(81-75)*12 because 75*1=75
so now, 75-(81*12-75*12) because 12 is outside bracket so it will be multiplied by both nos.
You must have heard that if minus sign is present before bracket then sign of no. Inside bracket changes. So,
75-81*12+75*12.
Take this as equation 1.
Now there are two 75
(1st no. in equation 1)->75 and then 75*12
75*12+75(the first no. In equation)
Do 75 *12+75
the result will be the same as 75*13
so it is written 75*13

In the last step it is written 237*13-38*81
since 237 and 81 are nos. You are finding h.c.f. Of and 13 and -38 are nos. Which will be multiplied by both nos. So x=13
y=-38

Answer 2

we have
75-(81-75*1)*12
75-(81-75)*12 because 75*1=75
so now, 75-(81*12-75*12)
 if minus sign is present before bracket then sign of no. Inside bracket changes. So,
75-81*12+75*12.
Take this as equation 1.
Now there are two 75
(1st no. in equation 1)->75 and then 75*12
75*12+75(the first no. In equation)
Do 75 *12+75
the result will be the same as 75*13
so it is written 75*13

In the last step it is written 237*13-38*81
since 237 and 81 are nos. You are finding h.c.f. Of and 13 and -38 are nos. Which will be multiplied by both nos. So x=13
y= - 38