Question

Solve the following inequalities
and write the solution set
using internal notation
i) x²- X>20

Answer 1

Question:

Solve the given inequality and write the solution set using interval notation.

• x² - x > 20

Answer:

x € (-∞,-4)U(5,∞)

Solution:

We have;

=> x^2 - x > 20

=> x^2 - x - 20 > 0

=> x^2 - 5x + 4x - 20 > 0

=> x(x - 5) + 4(x - 5) > 0

=> (x-5)(x+4) > 0

Two cases arises from the above inequation.

Case1 : (x-5) > 0 and (x+4) > 0

Case2 : (x-5) < 0 and (x+4) < 0

Case1 :

=> (x-5) > 0 and (x+4) > 0

=> x > 5 and x > - 4

=> x > 5

=> x € (5,∞)

Case2 :

=> (x-5) < 0 and (x+4) < 0

=> x < 5 and x < - 4

=> x < - 4

=> x € (-∞,-4)

Here,

The solution set of the given inequation will be given by the union set of case1 and case2.

Thus,

x € (-∞,-4)U(5,∞)

Hence,

Solution set :

x € (-∞,-4)U(5,∞)

Answer 2

Step-by-step explanation:

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