Question

(x² - 5)(x² - 4)
÷(x-1)
<=0​

Answer 1

Given:

(x² - 5) (x² - 4) ÷ (x - 1) <= 0​

To find:

(x² - 5) (x² - 4) ÷ (x - 1) <= 0​

Solution:

From given, we have,

(x² - 5) (x² - 4) ÷ (x - 1) <= 0​

we use the formula,

a² - b² = (a + b) (a - b)

(x - √5) (x + √5) (x - √4) (x + √4) ÷ (x - 1) <= 0​

(x - √5) (x + √5) (x - 2) (x + 2) ÷ (x - 1) <= 0​

x < - √5 or x = - √5

or x = -2 or -2 < x < 1 or x = 2

or 2 < x < √5 or x = √5

combining/overlapping all the intervals, we get,

∴ x ≤ - √5 or -2 ≤ x < 1 or 2 ≤ x ≤ √5