Solving the inequality x^2+7x>6+2x^3

[Gughanath]

x^2+7x>6+2x^3...I tried many times..i can't solve this ...please help

 

[Dr-NiKoN]

x^2 + 7x > 6 + 2x^3 = -2x^3 + x^2 + 7x - 6 > 0

Try solving for:
-2x^3 + x^2 + 7x - 6 = 0

 

[Gughanath]

x^2 + 7x > 6 + 2x^3 = -2x^3 + x^2 + 7x - 6 > 0

Try solving for:
-2x^3 + x^2 + 7x - 6 = 0

I can't solve that sorry...could you help any further?

 

[Tide]

I noticed the sum of the coefficients is 1 so (x-1) is a factor:

$$2x^3-x^2-7x+6 = (x-1)(x+2)(2x-3)$$

That should get you started!

 

[aekanshchumber]

try it,
x^2 + 7x>6x + 2x^3
or, 2x^3 - x^2 -x<0
or, x(2x^2 - x - 1)<0
this implies, either x<0 or (2x^2 - x - 1) <0
as the expression is negative which is only possible if one of the term is negative.

 

[Integral]

try it,
x^2 + 7x>6x + 2x^3
or, 2x^3 - x^2 -x<0
or, x(2x^2 - x - 1)<0
this implies, either x<0 or (2x^2 - x - 1) <0
as the expression is negative which is only possible if one of the term is negative.

You have read the problem incorrectly. It should read
$$x^2 + 7x > 6 + 2x^3$$