Xét hiệu :
\(100^2+103^2+105^2+94^2-\left(101^2+98^2+96^2+107^2\right)\)
\(=100^2+103^2+105^2+94^2-101^2-98^2-96^2-107^2\)
\(=\left(100^2-98^2\right)+\left(103^2+101^2\right)-\left(107^2-105^2\right)-\left(96^2-94^2\right)\)
\(=\left(100-98\right)\left(100+98\right)+\left(103-101\right)\left(103+101\right)-\left(96-94\right)\left(96+94\right)\)\(-\left(107-105\right)\left(107+105\right)\)
\(=2.198+2.204-2.212-2.190\)
\(=2.\left(198+204-212-190\right)\)
\(=2.0\)
\(=0\)
VẬY dpcm
Ta có:
1002+1032+1052+942=1012+982+962+1072
=>1002+1032+1052+942-(1012+982+962+1072)=0
=>1002+1032+1052+942-1012-982-962-1072=0
=>(1002-982) + (1032-1012) + (1052-1072) + (942-962) = 0
=>(100-98)(100+98) + (103-101)(103+101) + (105-107)(105+107) + (94-96)(94+96) = 0
=>2.(100+98) + 2.(103+101) - 2.(105+107) - 2.(94+96) = 0
=>2.[(100+98)+(103+101)-(105+107)-(94+96)] = 0
=>2.(198+204-212-190)=0
=>2.0=0
Chứng tỏ 1002+1032+1052+942=1012+982+962+1072
100^2+103^2+105^2+94^2=101^2+98^2+96^2+ 107^2
vt = 100^2+103^2+105^2+94^2
vp = 101^2+98^2+96^2+ 107^2
=> vp - vt = 101^2 - 100^2 + 98^2 - 103^2 + 96^2 -94^2 + 107^2 -105^2
= 201 - 201.5 + 190.2 + 212.2 = - 4.201 + 402.2 = - 4.201 + 4.201 = 0
=> vt = vp => đpcm
