Question

Solve x²-6x+8>0

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Answer 1

Answer:

▶ x € [ -∞ , 2 ] ∪ [ 4 , +∞ ]

Explanation:

Given that,

• x² - 6x + 8 > 0

[ Splitting middle term : We get, ]

▶x² - 2x - 4x + 8 > 0

▶x(x - 2) - 4(x - 2) > 0

▶(x - 2) (x - 4) > 0

▶{ (x - 2) > 0 , (x - 4) >0 }

▶{ (x - 2)<0 , (x - 4) <0}

▶{ (x > 2 ) , (x > 4) }

▶{ (x < 2 ) , (x < 4) }

▶ x € [ -∞ , 2 ] ∪ [ 4 , +∞ ]

Answer 2

Answer:

$\huge\rm{\fbox\color{lime}{Solution}}$

≈ x²- 6x + 8 = 0

≈ x = -(6) ± √(-6)² - 4 × 1 × 8 / 2

≈ x = 6 ± 2 /2

≈ x = 4

≈ x = 2

≈ (x - 4)(x - 2) > 0

≈ x - 4 < 0

≈ x - 2 < 0

≈ x < 2

≈ x - 2 > 0

≈ x - 4 > 0

≈ x > 4

x < 2 ; x > 4

Hence the required answer is x < 2 ; x > 4