Question

solve for x
basic inequality
class 11th
please answer me fast​

Answer 1

Answer:

ok

Step-by-step explanation:

Answer 2

EXPLANATION.

Complete set of :

⇒ (x² - 11x + 24)¹⁰¹/(x² - 10x + 24) ≤ 0.

As we know that,

First we factorizes numerator and denominator into middle term splits, we get.

Numerator = x² - 11x + 24.

⇒ x² - 8x - 3x + 24.

⇒ x(x - 8) - 3(x - 8).

⇒ (x - 3)(x - 8).

Denominator = x² - 10x + 24.

⇒ x² - 6x - 4x + 24.

⇒ x(x - 6) - 4(x - 6).

⇒ (x - 4)(x - 6).

We can write equation as,

⇒ (x - 3)¹⁰¹(x - 8)¹⁰¹/(x - 4)¹⁰⁰(x - 6)¹⁰⁰ ≤ 0.

First find the zeroes of the equation, we get.

⇒ (x - 3) = 0.

⇒ x = 3. - - - - - (1).

⇒ (x - 8) = 0.

⇒ x = 8. - - - - - (2).

⇒ (x - 4) = 0.

⇒ x = 4. - - - - - (3).

⇒ (x - 6) = 0.

⇒ x = 6. - - - - - (4).

Put this point on wavy curve method, we get.

If the power is odd then sign will change and the power is even then sign will not change.

The denominator is an even function of x, So denominator is always positive. Also the denominator vanishes at x = 4, 6.

Now,

⇒ x² - 11x + 24.

⇒ x² - 8x - 3x + 24.

⇒ x(x - 8) - 3(x - 8).

⇒ (x - 3)(x - 8).

⇒ (x - 3)(x - 8) ≤ 0.

⇒ 3 ≤ x ≤ 8.

We get,

⇒ x ∈ [3,8] - {4,6}.

Option [C] is correct answer.