Solve the inequality -
x² -7x + 12 / 2x² + 4x +5 > 0
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Answered by
1
★ INEQUALITIES ★
Given function :
x² -7x + 12/ 2x² + 4x + 5 > 0
x² - 4x -3x + 12 / 2x² + 4x + 5 > 0
( x - 3 )(x - 4 ) / 2x² +4x + 5 > 0
Hence ,
x ∈ ( -∞ , 3 ) ∪ ( 4 , + ∞ )
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Given function :
x² -7x + 12/ 2x² + 4x + 5 > 0
x² - 4x -3x + 12 / 2x² + 4x + 5 > 0
( x - 3 )(x - 4 ) / 2x² +4x + 5 > 0
Hence ,
x ∈ ( -∞ , 3 ) ∪ ( 4 , + ∞ )
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abhi178:
correct it
Answered by
4
now, numerator,
(2x² - 7x + 12)
first of all find discriminant
D = b² - 4ac
= (7)² - 4 × × 12
= 49 - 48 = 1
now,
(x² - 7x + 12)
= x² - 4x - 3x + 12
= (x -4)(x -3)
again for denominator,
(2x² + 4x + 5)
first we have to see discriminant of it
D = b² - 4ac = (4)² - 4 × 5 × 2
= 16 - 40 = -24 < 0
we know, if a >0 and D <0 then, ax² + bx + c >0 for all x ∈ R ,
hence, (2x² + 4x + 5) > 0 for all x ∈ R,
now,
(x - 3)(x - 4)/+ve >0
(x - 3)(x - 4) >0
x > 4 and x < 3
hence, x ∈ (-∞, 3) U (4, ∞)
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