SOLUTION: i need help with solving rational equations. how do you solve {{{ 2*sqrt(x^2-2)-sqrt(3x+7)<0}}}

Question 447752: i need help with solving rational equations. how do you solve
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

If you need help with rational equations, then why did you give an example of a radical inequality?

I'll help you with your example.

Step 1: Add

to both sides:

Step 2: Square both sides:

Step 3: Add

to both sides:

The left hand side is a quadratic trinomial. As a function, this trinomial has a graph that is a parabola that opens upward (+ lead coefficient). It also has 2 real number roots (either verify that the discriminant is >0 or note that the lead coefficient and the constant term are opposite signs). That means the vertex must be below the axis, hence the function is less than zero on the open interval between the two zeros. Use the quadratic formula to find the two zeros and thus the open endpoints of the solution interval.

John

My calculator said it, I believe it, that settles it

The Out Campaign: Scarlet Letter of Atheism

RELATED QUESTIONS
1) I need help in solving the following equations. a)sqrt x-2=1 b)sqrt... (answered by sarah_adam)

how do i solve... (answered by stanbon)

Solve the equations. 1) sqrt of x - 2 = 0 2) sqrt of 3x -6 = 0 (answered by jsmallt9)

Solve by completing the square. x^2 -14x +49 = 0 I came up with the answer of 7, 7 for... (answered by checkley75)

I need help with solving these equations can someone please show me how to solve them... (answered by EMStelley,MathTherapy)

I need help with 3x^2 - 2x + 1 = 0 I came out with x = 2/6 + sqrt 8/6 Did I do this (answered by fractalier)

How do I solve... (answered by Alan3354,josgarithmetic,MathTherapy)

Hi, I am having trouble solving quadratic equations. I get down to the bottom of the... (answered by jsmallt9)

I need help solving the following equation for 0(<=) X (<=)2pi 2sinXcosX= (sqrt... (answered by Fombitz)