a) (6x + 1)^2 + ( 6x - 1)^2 - 2(1 - 6x )( 6x - 1)
(6x + 1)^2-2 (6x + 1) (6x - 1)+ ( 6x - 1)^2
[ (6x + 1)- ( 6x - 1)^2 ]
(6x + 1-6x+1 )^2
2^2
=4
b)3(2^2 + 1) (2^4 + 1) (2^8 + 1) (2^16 + 1)
ta có 3=4-1=2^2-1
<=>(2^2 - 1)(2^2 + 1)(2^4 + 1)(2^8 + 1) (2^16 + 1)
=(2^4 -1) (2^4 + 1) (2^8 + 1) (2^16 + 1)
= (2^8 - 1)(2^8 + 1) (2^16 + 1)
= (2^16 - 1) (2^16 + 1)
=2^32-1
2
a )x^2 -2x.y+y^2+1
=(x -y)^2 +1
ta co (x -y)^2>=0 moi x va y
(x -y)^2 +1>0 moi x va y (dpcm)
2, x -x^2 -1 = -(x^2 -x+1) = -( x^2 -2.x.1/2+1/4 -1/4+1)= -(x-1/2)^2 -3/4
ta co -(x-1/2)^2 <= 0 moi x
b) x - x^2 - 1 < 0 với mọi số thực x
= - (x^2 - x + 1)
= - (x^2 - 2x.1/2 + 1/4 + 3/4)
= - (x-1/2)^2 - 3/4 ≤ -3/4 <0
=> dpcm