value question

Hy,

what is the value of x²-1?

1. x²-5x+6=0

2. x²-1=x+1


In my opinion, both statements resultate in 2 different solutions (each). So they are not suff. However, the OA says 2. would be suffic. Thank you for any help!

Should be C


combineing 1 and 2 there is only one value of x possible. x=2

OA is B. well, that's tricky.

x²-1=x+1

(x+1)(x-1)=x+1

x-1=1

x=1+1=2

so second statement is enough to answer the ques.

I think you need both a and b, to arrive at the value of x^2-1.
x^2-5x+6 = 0 implies x = 3 or 2, so x^2-1 is either 8 or 3
x^2-1=x+1 implies x= 2 or -1, so x^2-1 is either 3 or 0

So if you have both a and b, you can determine the value of x^2-1 to be 3. So, OA can't be B.

him_dah's explanation is almost correct, but when canceling x+1 on both sides, one of the solutions to the equation is being ignored (x=-1). Hope this helps.

It should be C.

you can cancel x+1 both the side, if and only x is not equal to -1, if it is then x + 1=0.
so for that x has two values again
x=-1 or x=2

hence, the only answers is C now.

@him_dah

your explantion holds wrong if x=-1
i.e
(-1+1)(-1-1)=-1+1
0*-2=0
you can not devide by 0 and bring 1

Answer is (B). the question stem says x={1,-1}

(a) provides x={3,2}
(b) provides x={-1,2}

Since the value x=-1 is present in (b). The answer is choice (B)

how does question stem say x={1,-1} ??

I am sorry ...i was wrong...The question stem doesn't say x={1,-1}.

Going by the below results, 2 is the correct answer(since that is the only common root)
(a) provides x={3,2}
(b) provides x={-1,2}

Answer Choice - (C)