Prove that if d is HCF of a and b then, d divides a-b and a+b.

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Solution

if d is the hcf of a and b,
i.e a÷d = an integer and b÷d= integer ....
ie a and b can divided by d without having reminder.

So (a+b)÷d = (a÷d)+(b÷d)
= integer + integer
= another integer.

so (a+b)÷d is also an integer which shows that a+b can be also divided by d.

similarly , (a-b)÷d
=a÷d - b÷d =integer- integer
=another integer.

this shows that a-b can be also divided by d.

so proved..

LIKE IF SATISFIED

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