The quadratic expression

[Albi]

[MATH][MATH]x_1_2 = \frac{a^2 + b^2 \pm \sqrt{a^4+2a^2b^2+b^4 – 4a^3b + 4ab^3}}{2(a^2 – b^2)}[\MATH][\MATH] Can someone tell me what can I do with the expsession in the square root.[/MATH][/MATH]

 

[JeffM]

[MATH]x_1^2 = \frac{a^2 + b^2 \pm \sqrt{a^4+2a^2b^2+b^4 – 4a^3b + 4ab^3}}{2(a^2 – b^2)}[/MATH]

Is this what you are talking about?

Try hitting “preview” before hitting “post.”

 

[Albi]

\displaystyle \(\displaystyle x_1_2 = \frac{a^2 + b^2 \pm \sqrt{a^4+2a^2b^2+b^4 – 4a^3b + 4ab^3}}{2(a^2 – b^2)}[\MATH][\MATH]

Is this what you are talking about?

Try hitting “preview” before hitting “post.”

Yes this is what I meant but not x1 squared

 

[Deleted member 4993]

Yes this is what I meant but not x1 squared

Use:

a⁴ + 2a²b² + b⁴ = (a² + b²)²

 

[JeffM]

Yes this is what I meant but not x1 squared

OK. We NOW know that is not the left hand side of the equation. Would you like to disclose what IS the left hand side, or shall I keep making guesses?

Perhaps x_1_2 means [MATH]x^{12}.[/MATH]
This may take a while if you continue so coy about saying what the equation actually is. There are an infinite number of things that it may not be.

 

[Albi]

OK. We NOW know that is not the left hand side of the equation. Would you like to disclose what IS the left hand side, or shall I keep making guesses?

Perhaps x_1_2 means [MATH]x^{12}.[/MATH]
This may take a while if you continue so coy about saying what the equation actually is. There are an infinite number of things that it may not be.

It is the quadratic formula

 

[Deleted member 4993]

It is the quadratic formula

I assume it is:

\(\displaystyle x_{1,2}\)

meaning x₁ or x₂.

 

[Otis]

… Can someone tell me what can I do with the [expression] in the square root.

Hi Albi. We call that one the "radicand".

In your equation, the radicand is a square, so we can factor it.

?

 

[JeffM]

It is the quadratic formula

The left hand side is not the quadratic formula. Did Subhotosh Khan guess correctly what you meant?

 

[Albi]

The left hand side is not the quadratic formula. Did Subhotosh Khan guess correctly what you meant?

Yes

 

[JeffM]

Then Otis and the Khan of Khans have already given you two suggestions for simplifying. Furthermore, I wonder whether you have reached the correct intermediate stage. You have not told us what led you to this rather messy equation.

[MATH][/MATH]

 

[Albi]

Then Otis and the Khan of Khans have already given you two suggestions for simplifying. Furthermore, I wonder whether you have reached the correct intermediate stage. You have not told us what led you to this rather messy equation.

[MATH][/MATH]

(a² -b²)x² -(a² +b²)x +ab = 0

 

[Steven G]

Why would you say what is wrong with the way JeffM wrote what he thought your equation was but not say what it should be? Things like this just puzzles me.

 

[JeffM]

If that is the only information that you were given, then

[MATH]x = \dfrac{(a^2 + b^2) \pm \sqrt{(a^2 + b^2)^2 - 4ab(a^2 - b^2)}}{2(a^2 - b^2)}[/MATH]
strikes me as an acceptable answer. You might consider whether further simplification results from

[MATH](a^2 + b^2) = (a + b)^2 - 2ab.[/MATH]
It MIGHT do so, but it looks like a lot of messy algebra without any assurance of a useful result.