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If-a-b-c-a-b-b-c-a-b-c-c-a-b-c-a-and-a-b-c-0-then-which-of-the-following-is-true-1-a-b-c-2-a-b-c-3-a-b-c-4-a-b-c-




Question Number 37037 by jayanta11 last updated on 08/Jun/18
If ((a+b−c)/(a+b)) = ((b+c−a)/(b+c)) =((c+a−b)/(c+a)) and   a+b+c ≠ 0 then which of the following  is true 1) a=−b=c 2)−a=−b=c   3) a=b=c 4) a=b≠c
Ifa+bca+b=b+cab+c=c+abc+aanda+b+c0thenwhichofthefollowingistrue1)a=b=c2)a=b=c3)a=b=c4)a=bc
Answered by math1967 last updated on 08/Jun/18
3)a=b=c  ((a+b)/(a+b))−(c/(a+b))=((b+c)/(b+c))−(a/(b+c))=((c+a)/(c+a))−(b/(c+a))  (c/(a+b))=(a/(b+c))=(b/(c+a))  ((a+b)/c)+1=((b+c)/a)+1=((c+a)/b)+1  ((a+b+c)/c)=((a+b+c)/a)=((a+b+c)/b)  (1/c)=(1/a)=(1/b)  [(a+b+c)≠0]  ∴c=a=b⇒a=b=c
3)a=b=ca+ba+bca+b=b+cb+cab+c=c+ac+abc+aca+b=ab+c=bc+aa+bc+1=b+ca+1=c+ab+1a+b+cc=a+b+ca=a+b+cb1c=1a=1b[(a+b+c)0]c=a=ba=b=c
Commented by Rasheed.Sindhi last updated on 08/Jun/18
Nice!
Nice!
Answered by Rasheed.Sindhi last updated on 08/Jun/18
((a+b−c)/(a+b)) = ((b+c−a)/(b+c)) =((c+a−b)/(c+a))               =(((a+b−c)+(b+c−a)+(c+a−b))/((a+b)+(b+c)+(c+a)))                    =((a+b+c)/(2(a+b+c)))=(1/2)  2(a+b−c)=a+b  2(b+c−a)=b+c  2(c+a−b)=c+a    a+b−2c=0⇒b=2c−a^∗   b+c−2a=0⇒2c−a+c−2a=0⇒3c=3a^∗   c+a−2b=0⇒c+a−4c+2a=0⇒3a=3c^∗   ^∗ a=b=c
a+bca+b=b+cab+c=c+abc+a=(a+bc)+(b+ca)+(c+ab)(a+b)+(b+c)+(c+a)=a+b+c2(a+b+c)=122(a+bc)=a+b2(b+ca)=b+c2(c+ab)=c+aa+b2c=0b=2cab+c2a=02ca+c2a=03c=3ac+a2b=0c+a4c+2a=03a=3ca=b=c
Answered by ajfour last updated on 08/Jun/18
((a+b−c)/(a+b))=((b+c−a)/(b+c))=((c+a−b)/(c+a))  ⇒  (c/(a+b))=(a/(b+c))=(b/(c+a))  ⇒  ((a+b+c)/c)=((a+b+c)/a)=((a+b+c)/b)  ⇒    a=b=c .
a+bca+b=b+cab+c=c+abc+aca+b=ab+c=bc+aa+b+cc=a+b+ca=a+b+cba=b=c.
Answered by tanmay.chaudhury50@gmail.com last updated on 08/Jun/18
((a+b−c)/(a+b))=((b+c−a)/(b+c))=((c+a−b)/(c+a))  1−(c/(a+b))=1−(a/(b+c))=1−(b/(c+a))  (c/(a+b))=(a/(b+c))=(b/(c+a))  bc+c^2 =a^2 +ab  bc−ab+c^2 −a^2 =0  b(c−a)+(c+a)(c−a)=0  (c−a)(b+c+a)=0  since a+b+c not equales to zero  so c=a  similarly a=b  so a=b=c  value of each ratio i  ((a+b−c)/(a+b))  =((a+a−a)/(a+a))  =(a/(2a))=(1/2)  value of each ratio  when a+b+c=0  ((a+b−c)/(a+b))  ((−c−c)/(−c))  ((−2c)/(−c))  =2
a+bca+b=b+cab+c=c+abc+a1ca+b=1ab+c=1bc+aca+b=ab+c=bc+abc+c2=a2+abbcab+c2a2=0b(ca)+(c+a)(ca)=0(ca)(b+c+a)=0sincea+b+cnotequalestozerosoc=asimilarlya=bsoa=b=cvalueofeachratioia+bca+b=a+aaa+a=a2a=12valueofeachratiowhena+b+c=0a+bca+bccc2cc=2

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