F.5數學題…唔明…

1.M=(a+b)/2
N=sqrt(ab)
(a+b)=2M,ab=N^2
(a-b)^2=(a+b)^2-4ab
=4M^2-4N^2
=4(M^2-N^2)
=4(M+N)(M-N)

5.P(at least one is good)=P(either one of them is good)+P(both good)
=(2/5)(3/4)+(3/5)(2/4)+(3/5)(2/4)
=9/10

1.) If M and N are the arithmetic and geometric means of a and b respectively,
express (a – b) 2 in terms of M and N.
1.M=(a+b)/2
N=sqrt(ab)
(a+b)=2M,ab=N^2
(a-b)^2=(a+b)^2-4ab
=4M^2-4N^2
=4(M^2-N^2)
=4(M+N)(M-N)

5. ) A box contains 5 apples , two of them are bad . If 2 apples are chosen at random without replacement , find probability that at least one of them is good .
5.P(at least one is good)=P(either one of them is good)+P(both good)
=(2/5)(3/4)+(3/5)(2/4)+(3/5)(2/4)
=9/10