Question

Find the smallest positive integral value satisfying :-

$\frac{(x - 1)( {x }^{2} - 9)}{x(x + 2)} < 0$
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Answer 1

Answer:

please go through solution sorry if any mistake done

Answer 2

EXPLANATION.

$\sf \implies \dfrac{(x - 1)(x^{2} - 9)}{x(x + 2)} < 0.$

As we know that,

We can write equation as,

$\sf \implies \dfrac{(x - 1)(x + 3)(x - 3)}{x(x + 2)} < 0$

Finding zeroes of the equation, we get.

⇒ x - 1 = 0.

⇒ x = 1. - - - - - (1).

⇒ x + 3 = 0.

⇒ x = -3. - - - - - (2).

⇒ x - 3 = 0.

⇒ x = 3. - - - - - (3).

⇒ x = 0. - - - - - (4).

⇒ x + 2 = 0.

⇒ x = -2. - - - - - (5).

Put the point on the wavy curve method, we get.

⇒ x ∈ (-∞,-3) ∪ (-2,0) ∪ (1,3).

Smallest positive integrals values = 2.

                                                                                                                         

MORE INFORMATION.

Explicit function.

A function is said to be explicit if it can be expressed directly in terms of the independent variable. y = f(x) or x = Ф(y).

Implicit form.

A function is said to be implicit if it can not be expressed directly in terms of the independent variable,

ax² + 2hxy + by² + 2gx + 2fy + c = 0.