Question

Solve for X: (x2 - 6x + 3)(x2 - 6x – 2) less than equal to 50​

Answer 1

we have to solve (x² - 6x + 3)(x² - 6x - 2) ≤ 50

let x² - 6x = t

⇒ (t + 3)(t - 2) ≤ 50

⇒t² + 3t - 2t - 6 ≤ 50

⇒t² + t - 6 ≤ 50

⇒t² + t - 56 ≤ 0

⇒t² + 8t - 7t - 56 ≤ 0

⇒t(t + 8) - 7(t + 8) ≤ 0

⇒(t - 7)(t + 8) ≤ 0

⇒-8 ≤ t ≤ 7

⇒ -8 ≤ x² - 6x ≤ 7

case 1 : x² - 6x ≥ -8

⇒x² - 6x + 8 ≥ 0

⇒x² - 4x - 2x + 8 ≥ 0

⇒(x - 4)(x - 2) ≥ 0

⇒x ≥ 4 , x ≤ 2

case 2 : x² - 6x ≤ 7

⇒x² - 6x - 7 ≤ 0

⇒x² - 7x + x - 7 ≤ 0

⇒(x - 7)(x + 1) ≤ 0

⇒ - 1 ≤ x ≤ 7

now x ≥ 4 , x ≤ -2 and - 1 ≤ x ≤ 7 putting in number line.

-1 ≤ x ≤ 2 , 4 ≤ x ≤ 7

therefore solution of given inequality is [-1, 2] U [4, 7]

Answer 2

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