MHB Yes, the correct solution would be to subtract (x/2) from both sides, not 2x.

  • Thread starter Thread starter mathdad
  • Start date Start date
  • Tags Tags
    Quadratic
mathdad
Messages
1,280
Reaction score
0
Solve the quadratic inequality.

2/x < x/2

Multiply both sides by 2x.

(2x)*(2/x) < (2x)(x/2)

4 < x^2

4 = x^2

sqrt{4} = sqrt{x^2}

-2 = x

2 = x

Our end points are -2 and 2.

<------(-2)----------(2)------->

For (-infinity, -2), let x = -3. In this interval, we get true.

For (-2, 2), let x = 0. In this interval, we get false.

For (2, infinity), let x = 3. In this interval, we get true.

Test the end points.

Let x = -2 and x = 2.

At x = -2, we get false.

At x = 2, we get false.

We exclude the test points.

Solution: (-infinity, -2) U (2, infinity)

Correct?
 
Mathematics news on Phys.org
RTCNTC said:
Solve the quadratic inequality.

2/x < x/2

Multiply both sides by 2x.

You are assuming x is positive when you do that. A better step is to subtract x/2 from both sides:

$$\frac{2}{x}-\frac{x}{2}<0$$

Combine terms:

$$\frac{4-x^2}{2x}<0$$

$$\frac{(2+x)(2-x)}{2x}<0$$

Now we see we have 3 critical values which give us 4 intervals:

$$(-\infty,-2)$$ Test value: x = -3: expression is (-)(+)/(-) = + not part of solution. Other intervals will alternate...

$$(-2,0)$$ is part of solution.

$$(0,2)$$ not part of solution.

$$(2,\infty)$$ is part of solution.

And so the solution is:

$$(-2,0)\,\cup\,(2,\infty)$$
 
You meant to say subtract (x/2) from both sides not 2x.
 
Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...
Fermat's Last Theorem has long been one of the most famous mathematical problems, and is now one of the most famous theorems. It simply states that the equation $$ a^n+b^n=c^n $$ has no solutions with positive integers if ##n>2.## It was named after Pierre de Fermat (1607-1665). The problem itself stems from the book Arithmetica by Diophantus of Alexandria. It gained popularity because Fermat noted in his copy "Cubum autem in duos cubos, aut quadratoquadratum in duos quadratoquadratos, et...
I'm interested to know whether the equation $$1 = 2 - \frac{1}{2 - \frac{1}{2 - \cdots}}$$ is true or not. It can be shown easily that if the continued fraction converges, it cannot converge to anything else than 1. It seems that if the continued fraction converges, the convergence is very slow. The apparent slowness of the convergence makes it difficult to estimate the presence of true convergence numerically. At the moment I don't know whether this converges or not.

Similar threads

Back
Top