CameraIcon

SearchIcon

MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Summation by Sigma Method

Solve the fol...

Question

Solve the following inequality:
$(x^{2} + 3 x) (2 x + 3) - 16 \frac{2 x + 3}{x^{2} + 3 x} ⩾ 0$

Open in App

Solution

$(x^{2} + 3 x) (2 x + 3) - 16 \frac{2 x + 3}{x^{2} + 3 x} \geq 0$
$(2 x + 3) \frac{((x^{2} + 3 x)^{2} - 4^{2})}{x (x + 3)} \geq 0$
$\frac{(2 x + 3) (x^{2} + 3 x - 4) ((x + \frac{3}{2})^{2} + \frac{5}{4})}{x (x + 3)} \geq 0$
$(x + 4) (x + 3) (2 x + 3) x (x - 1) \geq 0$
$⟹ x \in [- 4, - 3] \cup [- 3 / 2, 0] \cup [3, \infty)$

Suggest Corrections

thumbs-up

0

Similar questions

(X^{2} + 3 X) (2 X + 3) - 16 \frac{2 X + 3}{X^{2} + 3 X} \geq 0

(x^{2} + 3 x) (2 x + 3) - 16 \frac{2 x + 3}{x^{2} + 3 x} \geq 0

(x^{2} + 3 x) (2 x + 3) - 16 \frac{2 x + 3}{x^{2} + 3 x}

Q. Solve the following inequality:

(x^{2} + 3 x + 1) (x^{2} + 3 x - 3) ⩾ 5

Q. Solve the following inequality:

\frac{x^{2} - 3 x + 24}{x^{2} - 3 x + 3} < 4

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Summation by Sigma Method

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Summation by Sigma Method

Standard XII Mathematics

Join BYJU'S Learning Program

CrossIcon