F.4 math-.-.-.-.-.-.-15marks

1.It is given that m + (1/m)= 2√3. Find the value of each of the following.
(a) m^2 + [1 / (m^2)]
= m^2 +2+ [1 / (m^2)]－2
=(m+1/m)^2－2
=(2√3)^2－2
=12－2
=10

(b) m－(1/m)
Set p=m－(1/m)
p^2=m^2－2+(1/m^2)=8
p=+/-2√2

(c) m^2－ [1 / (m^2)]
=[ m + (1/m)]*[ m－(1/m)]
=+/-4√6

2.It is known that the hundreds, tens and units digits ofa three-digit number are a, b and c
respectively.
(a) Express the value of the three-digit number in termsof a,b and c.
100a+10b+c

(b) If the three-digit number is a multiple of 3, provethat a+b+c is a multiple of 3.
3|( 100a +10b+c)
=>3|( 99a +9b+a+b+c)
=>3|(a+b+c)

(c) If a+b+c is a multiple of 3, prove that thethree-digit number is a multiple of 3.
3|(a+b+c)，3|( 99a +9b)
=>3|(a+b+c+ 99a +9b)
=>3|( 100a +10b+c)