ection 'EQuestion mumbers 7 to 12 carry 2 marks each.Show that any positive even integer can be written in the form 6, 6+2 or 6+ 4, where g is an integer.w that any positive even integer can be written in the form 6q,x2 + 7x + 512 =0

ection 'EQuestion mumbers 7 to 12 carry 2 marks each.Show that any pos

1.	ection 'EQuestion mumbers 7 to 12 carry 2 marks each.Show that any positive even integer can be written in the form 6, 6+2 or 6+ 4, where g is an integer.w that any positive even integer can be written in the form 6q,x2 + 7x + 512 =0
Answer» Let ‘a’ be any positive even integer and ‘b= 6’.Therefore,a = 6q +r, where 0≤r < 6.Now, by placing r = 0, we get, a = 6q + 0 = 6qBy placing r = 1, we get, a = 6q +1By placing, r = 2, we get, a = 6q + 2By placing, r = 3, we get, a = 6q + 3By placing, r = 4, we get, a = 6q + 4By placing, r = 5, we get, a = 6q +5Thus, a = 6q or, 6q +1 or, 6q + 2 or, 6q + 3 or, 6q + 4 or, 6q +5.But here, 6q +1, 6q + 3, 6q +5 are the odd integers.Therefore, 6q or, 6q + 2 or, 6q + 4 are the forms of any positive even integers.