等差数列中a1+a2+a3+a4+a5=3,a1*a1+a2*a2+a3*a3+a4*a4+a5*a5=12求a1-a2+a3-a4+a5

a1+a2+a3+a4+a5=3
a1+a2=a3-d+a3-2d=2a3-3d
a4+a5=a3+d+a3+2d=2a3+3d
a1+a2+a3+a4+a5=2a3-3d+2a3+3d+a3=3
5a3=3
a3=3/5
a1^2+a2^2+a3^2+a4^2+a5^2=12
a1=a3-2d
a2=a3-d
a4=a3+d
a5=a3+2d
a1^2+a2^2=(a3-d)^2+(a3-2d)^2=2a3^2-6a3d+5d^2
a4^2+a5^2=(a3+d)^2+(a3+2d)^2=2a3^2+6a3d+5d^2
a1^2+a2^2+a3^2+a4^2+a5^2=2a^3-6a3d+5d^2+2a^2+6a3d+5d^2+a3^2=12
5a3^2+10d^2=12
d=3(√10)/10
a1-a2=-d,a3-a4=-d,a5-a6=-d
a1-a2+a3-a4+a5-a6=-3d=(-9√10)/10

楼上没做完啊a1+a2+a3+a4+a5=3,...① a1^2+a2^2+a3^2+a4^2+a5^2=12,...② 则a1-a2+a3-a4+a5=x...③ 设①式等比为q,则②式为q^2,③式为-q 由等比求和公式,①式可化为a1(1-q^5)/(1-q)=3 ②式可化为a1^2(1-q^10)/(1-q^2...