Question

Rút gọn biểu thức:P=12(5^2+1)(5^4+1)(5^8+1)(5^16+1)

CM đẳng thức: (a+b+c)^3= a^3+b^3+c^3+3(a+b)(b+c)(c+a)

 

Answer 1

(a+b+c)³=(a+b)³+3(a+b)²c+3(a+b)c²+c³

=a³+b³+3ab.(a+b)+3(a+b)²c+3(a+b)c²+c³

=a³+b³+c³+3(a+b)(ab+ac+bc+c²)

=a³+b³+c³+3(a+b)[a.(b+c)+c.(b+c)]

=a³+b³+c³+3(a+b)(b+c)(c+a) 

=>dpcm

Answer 2

 

P=12(5^2+1)(5^4+1)(5^8+1)(5^16+1)

=>2P=24(5^2+1)(5^4+1)(5^8+1)(5^16+1)

=(5²-1)(5²+1)(5⁴+1)(5⁸+1)(5¹⁶+1)

=(5⁴-1)(5⁴+1)(5⁸+1)(5¹⁶+1)

=(5⁸-1)(5⁸+1)(5¹⁶+1)

=(5¹⁶-1)(5¹⁶+1)

=5³²-1

==>P=(5³²-1)/2

 

 

Answer 3

thanks anh Triều!