What is the solution for the inequation x^2 - x - 6 > 0
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calendarEducator since 2010
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We need to find x that satisfies x^2 - x - 6 > 0
x^2 - x - 6 > 0
=> x^2 – 3x + 2x – 6 > 0
=> x(x – 3) + 2(x – 3) > 0
=> (x + 2) (x – 3) > 0
For this to be valid either both (x + 2) and (x – 3) should be greater than 0 or both (x + 2) and (x – 3) should be less than 0.
In the first case (x + 2) > 0 and (x – 3) > 0
=> x > -2 and x > 3
x > 3 satisfies both the conditions.
In the second case (x + 2) < 0 and (x – 3) < 0
=> x < -2 and x < 3
x < -2 satisfies both the conditions.
This gives us the values of x as either greater than 3 or less than -2.
The required values of x lie in (-inf, - 2) U (3, inf)
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calendarEducator since 2008
write3,662 answers
starTop subjects are Math, Science, and Social Sciences
x^2- x - 6 > 0
First we will factor the left side.
==> (x-3)(x+2) > 0
Now we have a product of two terms.
In order for the product to be positive, then both terms should be positive or both terms should be negative.
Then we will write:
x-3 > 0 AND x+2 > 0
==> x > 3 AND x > -2
==> x = ( 3, inf ) n (-2, inf) = (3,inf) ..........(1)
Now for the other option, both terms are negative.
==> x-3 < 0 AND x+ 2 < 0
==> x < 3 AND x < -2
==> x = ( -inf, 3) n ( -inf , -2) = ( -inf, -2)............(2)
Then, from (1) and (2) we have two solutions:
==> x = ( -inf , -2) U ( 3, inf)
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