Toán Lớp 8: Tính: a) 24( $5^{2}$ +1 )( $5^{4}$ +1 )( $5^{8}$ +1 )-..( $5^{256}$ + 1 ) b) 4( $3^{2}$ + 1 )( $3^{4}$ + 1 )( $3^{8}$ + 1 )-( $3^

Question

Toán Lớp 8:  Tính: a) 24( $5^{2}$ +1 )( $5^{4}$ +1 )( $5^{8}$ +1 )......( $5^{256}$ + 1 ) b) 4( $3^{2}$ + 1 )( $3^{4}$ + 1 )( $3^{8}$ + 1 )....( $3^{512}$ + 1 )

maianhtuanh · Answer

Giải đáp+Lời giải và giải thích chi tiết:     a)24(5^2+1)(5^4+1)(5^8+1).......(5^256+1)   =(25-1)(5^2+1)(5^4+1)(5^8+1).......(5^256+1)   =(5^2-1)(5^2+1)(5^4+1)(5^8+1).......(5^256+1)   =(5^4-1)(5^4+1)(5^8+1).......(5^256+1)   =(5^8-1)(5^8+1).......(5^256+1)   =(5^16-1)......(5^256+1)   =(5^256-1)(5^256+1)   =5^512-1   b)4(3^2+1)(3^4+1)(3^8+1).......(3^512+1)   =(2.4(3^2+1)(3^4+1)(3^8+1).......(3^512+1))/2   =(8.(3^2+1)(3^4+1)(3^8+1).......(3^512+1))/2   =((9-1)(3^2+1)(3^4+1)(3^8+1).......(3^512+1))/2   =((3^2-1)(3^2+1)(3^4+1)(3^8+1).......(3^512+1))/2   =((3^4-1)(3^4+1)(3^8+1).......(3^512+1))/2   =((3^8-1)(3^8+1).......(3^512+1))/2   =((3^16-1).......(3^512+1))/2   =((3^512-1)(3^512+1))/2   =(3^1024-1)/2