求解(a + b-x)/ c +(a + c-x)/ b +(c + b-x)/ a +(4x)/(a + b + c)= 1?

求解(a + b-x)/ c +(a + c-x)/ b +(c + b-x)/ a +(4x)/(a + b + c)= 1?
Anonim

#(A + B-X)/ C +(A + C-X)/ B +(C + B-X)/ A +(4×)/(A + B + C)= 1#

#=>(A + BX)/ C + 1 +(A + CX)/ B + 1 +(C + BX)/ A + 1 +(4×)/(A + B + C)-3-1 = 0 #

#=>(A + B + C-X)/ C +(A + C + B-X)/ B +(C + B + A-X)/ A-4(1-X /(A + B + C))= 0#

#=>(A + B + C-X)(1 / C + 1 / B + 1 / A)-4((A + B + C-X)/(A + B + C))= 0#

#=>(A + B + C-X)(1 / C + 1 / B + 1 / A-4 /(A + B + C))= 0#

所以

#=>(A + B + C-X)= 0#

对于 #(1 / C + 1 / B + 1 / A-4 /(A + B + C))!= 0#

于是 #X = A + B + C#