The number of integer values of 'x' satisfying x^2 - 4x + 2 / x^2 - x - 30 Less than or Equal to 0 is
Answers
Given : (x²- 4x + 2) / (x² - x - 30) ≤ 0
To Find : The number of integer values of 'x'
Solution:
(x² - 4x + 2) / (x² - x - 30) ≤ 0
Case 1 :
x² - 4x + 2 = 0 and x² - x - 30 ≠ 0
=> no integral value of x , (x - 6)(x + 5) = 0 => x ≠ 6 , - 5
Case 2 :
x² - 4x + 2 > 0 and x² - x - 30 < 0
(x - 2)² - 2 > 0 (x - 6)(x + 5) < 0
(x - 2)² > 2 - 5 < x < 6
=> x - 2 > √2
=> x > 2 + √2
=> x ≥ 4 for integral values
or x - 2 < - √2
=> x < 2 - √2
=> x ≤ 0 for integral values
x ≥ 4 , x ≤ 0
- 5 < x < 6
- 4 , - 3 , - 2 , - 1 , 0 , 4 , 5
Case 3 :
x² - 4x + 2 < 0 and x² - x - 30 > 0
(x - 2)² - 2 < 0 (x - 6)(x + 5) > 0
(x - 2)² < 2 x < - 5 and x > 6
=> -√2 < x - 2 < √2
=> 2 - √2 < x < 2 + √2
1 ≤ x ≤ 3 for integral values
x < - 5 and x > 6
no common solution
- 4 , - 3 , - 2 , - 1 , 0 , 4 , 5
Hence 7 integral values of 'x'
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