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Question
Solve the following inequality and write the solution set using interval notation
x2 − x > 20
Solution
x2 − x > 20
∴ `x^2 - x + 1/4 > 20 + 1/4`
∴ `(x - 1/2)^2 > 81/4 = (9/2)^2`
∴ `x - 1/2 < - 9/2` or `x - 1/2 > 9/2`
∴ `x < - 9/2 + 1/2` or `x > 9/2 + 1/2`
∴ x < − 4 or x > 5
∴ solution set is `( - ∞, - 4) ∪ (5, ∞)`
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