x² - 1 < = 0 and x²- x - 2 > = 0, then x lies in the interval/set
A. (-1, 2)
B.(-1, 1)
C. (1, 2)
D. {-1}.
E. (1, -2)
A. (-1, 2)
B.(-1, 1)
C. (1, 2)
D. {-1}.
E. (1, -2)
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x^2 - 1 <= 0 => (x-1)(x+1) <=0 => -1<=x<=1Night reader wrote:x² - 1 < = 0 and x²- x - 2 > = 0, then x lies in the interval/set
A. (-1, 2)
B.(-1, 1)
C. (1, 2)
D. {-1}.
E. (1, -2)
There is a mistake. Check with x=0 (which lies in -1<=x<=1) for both the equations.Night reader wrote:I think the answer is B, though this problem has been posted at other forums without OA and answered D
x^2 - 1 =< 0
|x|=<1, -1 =< x =< 1
intervals
{-infin}___+ve___{-1}___-ve___{1}___+ve___{+infin}
x^2 - x - 2 >= 0
(x-2)(x+1) >= 0
(I omit the individual inequality solutions to save space)
intervals
{-infin}___+ve___{-1}___-ve___{1}___-ve___{2}___+ve___{+infin}
it would be good to have a normal picture for better visualizing
So answer is B, because the common solution area is (-1, 1)
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