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stat 1: suff.. factorise the given equation and get the answer

stat 2 : not suff

ans A
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What is the sum \(a+b+c\)?

(1) \(x^3−x=(x+a)(x+b)(x+c)\) for all values \(x\)
(2) \(a=b+1\) and \(c=a+1\)
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ziyuenlau
What is the sum \(a+b+c\)?

(1) \(x^3−x=(x+a)(x+b)(x+c)\) for all values \(x\)
(2) \(a=b+1\) and \(c=a+1\)


Let's see the statements..

(1) \(x^3−x=(x+a)(x+b)(x+c)\) for all values \(x\)
\(x^3-x=x(x^2-1)=x(x-1)(x+1)\)...
So \(x(x-1)(x+1)=(x+a)(x+b)(x+c)\)......=> a, b and c are roots of the equation and 0,1 and -1 are also roots ..
Thus a+b+c=0+1+(-1)=0
Sufficient

(2) \(a=b+1\) and \(c=a+1\)[/quote]
We will get the answer in terms of a variable..
Insufficient

A
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ziyuenlau
What is the sum \(a+b+c\)?

(1) \(x^3−x=(x+a)(x+b)(x+c)\) for all values \(x\)
(2) \(a=b+1\) and \(c=a+1\)

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