Question

Hey maths... Solve this linear inequality with the help of wavy curve method.... Plzzzzz.. Its urgent..
X^2+4x+4/2x^2-x-1>0

No spams..

Answer 1

Let f(x) = (x² + 4x + 4)/(2x² - x - 1) > 0

step1 : first of all, individually resolving numerator and denominator.

numerator : x² + 4x + 4 = x² + 2.2x + 2²

= (x + 2)²

denominator : 2x² - x - 1 = 2x² - 2x + x - 1

= 2x(x - 1) + 1(x - 1)

= (2x + 1)(x - 1)

step2: now, equate all of these to zero,

(x + 2)² = 0 => x = -2

(2x + 1)(x - 1) => x = -1/2 , 1

step3: put all values of x in number line.

now check, for x > 1 => f(x) > 0

for -1/2 < x < 1 => f(x) < 0

for -2 ≤ x < -1/2 => f(x) > 0

for x < -2 => f(x) > 0

all value of x where f(x) > 0 will contain our solution.

so, solution is x > 1 or, -2 ≤ x < -1/2 or, x < -2

or , $x\in(1,\infty)\cup[-2,-1/2)\cup(-\infty,-2)$

or, $x\in(1,\infty)\cup(-\infty,-1/2)$