Question
If ab+c=bc+a=ca+b=r then, r cannot take any value except :(CAT 2004)
Answer: Option C
:
C
Option (c)
As ab+c=bc+a=ca+b=a+b+cb+c+c+a+a+b
=a+b+c2(a+b+c)=r=12 (Assuming a + b + c ≠ 0)
If a + b + c = 0
ab+c = aa+b+c−a (by adding and subtracting a in the denominator) =a0−a=a−a=r=−1
(similarly bc+a=ca+b= -1)
Hence r can take only 12 or -1 as values. Choice (c)
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:
C
Option (c)
As ab+c=bc+a=ca+b=a+b+cb+c+c+a+a+b
=a+b+c2(a+b+c)=r=12 (Assuming a + b + c ≠ 0)
If a + b + c = 0
ab+c = aa+b+c−a (by adding and subtracting a in the denominator) =a0−a=a−a=r=−1
(similarly bc+a=ca+b= -1)
Hence r can take only 12 or -1 as values. Choice (c)
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