If x2
– 5x + 8 is positive, then find range of x.
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Given : x² - 5x + 8 is positive
To Find : Range of x
Solution:
x² - 5x + 8 is positive
=> x² - 5x + 8 >0
=> x² -5x + (5/2)² - (5/2)² + 8 > 0
=> ( x - 5/2)² - 25/4 + 8 > 0
=> (x - 5/2)² + 7/4 > 0
=> (x - 5/2)² > - 7/4
(x - 5/2)² ≥ 0
0 > -7/4
Hence inequality is true for all values of x
Range of x ∈ R (-∞ , ∞ )
Range of x² - 5x + 8 (7/4 , ∞)
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