Question

Here we are providing the questions which are important as per the CBSE board exam for class 10 chapter 1
Students can practice these questions and tally their answers with the provided answers here.
Q.1: Use Euclid's division lemma to show that the square of any positive integer is either of the form 3m or 3m
+ 1 for some integer m.​

Answer 1

Answer:

let a be a positive integer

on dividing a by 3

by Euclid division lemma

a=3q+ r

take r=0

a=3q+ r

a=3q+0

a=3q

squaring both side

a²=(3q) ²

a²=9q²

a²=3(3q²)

a²=3m(where m=3q²)

r=1

a=3q+r

a=3q+1

squaring both sides

a²=(3q+1) ²

a²=9q²+6q+1

a²=3(3q²+2q) +1

a²=3m+1(where m=3q²+2q)