Grade 12Algebra
if (a+1)(b+1)(c+1)=4 abc prove that a+b+c=abcplz help me fast guys exams are near
if (a+1)(b+1)(c+1)=4 abc prove that a+b+c=abc
plz help me fast guys exams are near
6 Answers
Vikas TU
Multiply all the three terms and get,
(a+b+c) + (ab + bc +ca) = abc + 2abc
now from property:
(ab +bc +ca) = 2abc
hence,
a+b+c=abc
Ajay
How is this statement true? Neither the question nor answer seem to be correct.
now from property:
(ab +bc +ca) = 2abc
Vikas TU
the qstn. is somewhat partially incompleted.
he should have given one more relation just like similar to what i already meant used.
he should have given one more relation just like similar to what i already meant used.
by my side.
Ankit Jaiswal
i am sorry about it but i thought it will not help actually in the question it also given that a,b,c are 3 different +ve integers
mycroft holmes
Write the equation as Suppose And so So we have c =1.The equation becomes (1+a)(1+b) = 2ab or 1+a+b = ab.Since a divides ab and a, we have a divides (b+1) and similarly b divides a+1.This yields Also a divides b+1 means a is not equal to b (as b does not divide b+1). So a = b+1.So the equation (a+1)(b+1) = 2ab now becomes a(a+1) = 2a (a-1) so a=3, and b=2.So (a,b,c) = (3,2,1) is the only solution. This solution satisfies the relation a+b+c=abc
mycroft holmes
Write the equation as 
Suppose 
And so
So we have c =1.
The equation becomes (1+a)(1+b) = 2ab or 1+a+b = ab.
Since a divides ab and a, we have a divides (b+1) and similarly b divides a+1.
This yields 
Also a divides b+1 means a is not equal to b (as b does not divide b+1). So a = b+1.
So the equation (a+1)(b+1) = 2ab now becomes a(a+1) = 2a (a-1) so a=3, and b=2.
So (a,b,c) = (3,2,1) is the only solution. This solution satisfies the relation a+b+c=abc
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