Question

Show that the square of any positive integer cannot be of the form 6m + 2 or 6m + 5 for
any integer m.
(NCERT EXEMPLAR)​

Answer 1

Answer:

60m+25=24m+4

m=-21/36=-7/12

Answer 2

When r= 0, a²= (6q)²

a²= 36q²= 6(6q²)= 6m, (m=6q²)

when r=1, a²= (6q+1)²

a²= 36q²+12q+1 = 6(6q²+2q)+1 = 6m+1,(m=6q²+2q)

When r= 2, a²= (6q+2)²

a²= 36q²+24q+4= 6(6q²+4q)+4 = 6m+4,(m=6q²+4q)

when r= 3, a²=(6q+3)²

a²=36q²+36q+9= 6(6q²+6q+1)+3= 6m+3,(m=6q²+6q+1)

when r=4, a²= (6q+4)²

a²=36q²+48q+16= 6(6q²+6q+2)+3=6m+3,(m=6q²+6q+2)

when r=5, a²=(6q+5)²

a²=36q²+60q+25=6(6q²+10q+4)+1=6m+1m=(6q²+10q+4)

Hence, from the above cases we see that the square of any positive integer cannot be of the form 6m + 2 or 6m + 5 for any integer m.

HOPE THIS HELPS!

I AM ALSO IN CLASS 10th AND I AM ALSO DOING EXEMPLAR QUESTIONS.