23.式子a(1/b+1/c)+b(1/c+1/a)+c(1/a+1/b)有意义且值为-3 证明:(1)abc≠0,且a^2+b^2+c^2-ab-bc-ca=0 =/=>a(1/b+1/c)+b(1/c+1/a)+c(1/a+1/b)有意义且值为-3 (2)a+b+c=0 =/=>a(1/b+1/c)+b(1/c+1/a)+c(1/a+1/b)有意义且值为-3 (3)abc≠0,a^2+b^
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![23.式子a(1/b+1/c)+b(1/c+1/a)+c(1/a+1/b)有意义且值为-3 证明:(1)abc≠0,且a^2+b^2+c^2-ab-bc-ca=0 =/=>a(1/b+1/c)+b(1/c+1/a)+c(1/a+1/b)有意义且值为-3 (2)a+b+c=0 =/=>a(1/b+1/c)+b(1/c+1/a)+c(1/a+1/b)有意义且值为-3 (3)abc≠0,a^2+b^](/uploads/image/z/9414574-70-4.jpg?t=23.%E5%BC%8F%E5%AD%90a%281%2Fb%2B1%2Fc%29%2Bb%281%2Fc%2B1%2Fa%29%2Bc%281%2Fa%2B1%2Fb%29%E6%9C%89%E6%84%8F%E4%B9%89%E4%B8%94%E5%80%BC%E4%B8%BA-3+%E8%AF%81%E6%98%8E%EF%BC%9A%281%29abc%E2%89%A00%2C%E4%B8%94a%5E2%2Bb%5E2%2Bc%5E2-ab-bc-ca%3D0+%3D%2F%3D%3Ea%281%2Fb%2B1%2Fc%29%2Bb%281%2Fc%2B1%2Fa%29%2Bc%281%2Fa%2B1%2Fb%29%E6%9C%89%E6%84%8F%E4%B9%89%E4%B8%94%E5%80%BC%E4%B8%BA-3+%282%29a%2Bb%2Bc%3D0+%3D%2F%3D%3Ea%281%2Fb%2B1%2Fc%29%2Bb%281%2Fc%2B1%2Fa%29%2Bc%281%2Fa%2B1%2Fb%29%E6%9C%89%E6%84%8F%E4%B9%89%E4%B8%94%E5%80%BC%E4%B8%BA-3+%283%29abc%E2%89%A00%2Ca%5E2%2Bb%5E)
23.式子a(1/b+1/c)+b(1/c+1/a)+c(1/a+1/b)有意义且值为-3 证明:(1)abc≠0,且a^2+b^2+c^2-ab-bc-ca=0 =/=>a(1/b+1/c)+b(1/c+1/a)+c(1/a+1/b)有意义且值为-3 (2)a+b+c=0 =/=>a(1/b+1/c)+b(1/c+1/a)+c(1/a+1/b)有意义且值为-3 (3)abc≠0,a^2+b^
23.式子a(1/b+1/c)+b(1/c+1/a)+c(1/a+1/b)有意义且值为-3
证明:(1)abc≠0,且a^2+b^2+c^2-ab-bc-ca=0 =/=>a(1/b+1/c)+b(1/c+1/a)+c(1/a+1/b)
有意义且值为-3 (2)
a+b+c=0 =/=>a(1/b+1/c)+b(1/c+1/a)+c(1/a+1/b)有意义且值为-3
(3)abc≠0,a^2+b^2+c^2-ab-bc-ca=0,且a+b+c=0 =/=>a(1/b+1/c)+b(1/c+1/a)+c
(1/a+1/b)有意义且值为-3
24.(a+b)/(c+d)=√(a^2+b^2)/√(c^2+d^2)
证明:(1)a/b=c/d,且b,d 均为正数 ==> (a+b)/(c+d)=√(a^2+b^2)/√(c^2+d^2)(2)
a/b=c/d,且b,d 均为负数 ==> (a+b)/(c+d)=√(a^2+b^2)/√(c^2+d^2)
23.式子a(1/b+1/c)+b(1/c+1/a)+c(1/a+1/b)有意义且值为-3 证明:(1)abc≠0,且a^2+b^2+c^2-ab-bc-ca=0 =/=>a(1/b+1/c)+b(1/c+1/a)+c(1/a+1/b)有意义且值为-3 (2)a+b+c=0 =/=>a(1/b+1/c)+b(1/c+1/a)+c(1/a+1/b)有意义且值为-3 (3)abc≠0,a^2+b^
证明:(1)若A,B,C其中一个是0,则a(1/b+1/c)+b(1/c+1/a)+c(1/a+1/b)不成立或无意义,所以abc≠0
a^2+b^2+c^2-ab-bc-ca=0
2*(a^2+b^2+c^2-ab-bc-ca)=2*0
2*a^2+2*b^2+2*c^2-2*ab-2*bc-2*ca=0
a^2+b^2-2*ab+a^2+c^2-2*ca+b^2+c^2-2*bc=0
(a+b)^2+(a+c)^2+(b+c)^2=0
a(1/b+1/c)+b(1/c+1/a)+c(1/a+1/b)=-3
所以a^2+b^2+c^2-ab-bc-ca=0 =/=>a(1/b+1/c)+b(1/c+1/a)+c(1/a+1/b)