I expanded it, and by hit and trial method, -1 was the solution. Then I divided the expanded polynomial by (x+1). The resultant cubic can be easily factorised.

@Mục Xiên
–
well, we want to start to factorize the polynomial. You can use the rational root theorem
to guess at possible roots, and after which use the remainder factor theorem to help factorize. Have you seen these theorems before?

@Calvin Lin
–
Well, I think I haven't seen these theorems before. Because I'm a middle school students.
BTW, I'll ask my teacher for this problem's explaination, thanks for your helps!

Easy Math Editor

`*italics*`

or`_italics_`

italics`**bold**`

or`__bold__`

boldNote: you must add a full line of space before and after lists for them to show up correctlyparagraph 1

paragraph 2

`[example link](https://brilliant.org)`

`> This is a quote`

Remember to wrap math in \( ... \) or \[ ... \] to ensure proper formatting.`2 \times 3`

`2^{34}`

`a_{i-1}`

`\frac{2}{3}`

`\sqrt{2}`

`\sum_{i=1}^3`

`\sin \theta`

`\boxed{123}`

## Comments

Sort by:

TopNewest\( x = y + 1\)

\( ( y + 1)^2 + (\dfrac{y + 1}{y})^2 = \dfrac{5}{4}\)

\( y^2 + 2y + 1 + 1 + \dfrac{1}{y^2} + \dfrac{2}{y} = \dfrac{5}{4}\)

\( y^2 + \dfrac{1}{y^2} + 2y + \dfrac{2}{y} + 2 = \dfrac{5}{4}\)

\( a = y + \dfrac{1}{y}\)

\( a^2 - 2 + 2a + 2 = \dfrac{5}{4}\)

\( (a + 1)^2 = (\pm \dfrac{3}{2})^2\)

\( a = - \dfrac{5}{2} , \dfrac{1}{2}\)

\( y + \dfrac{1}{y} = - \dfrac{5}{2} , y + \dfrac{1}{y} = \dfrac{1}{2}\)

\( y = \dfrac{ -\dfrac{5}{2} \pm \sqrt{\dfrac{9}{4}}}{2} , y = \dfrac{ \dfrac{1}{2} \pm i\sqrt{\dfrac{15}{4}}}{2}\)

\( x - 1 = \dfrac{ -\dfrac{5}{2} \pm \sqrt{\dfrac{9}{4}}}{2} , x - 1 = \dfrac{ \dfrac{1}{2} \pm i\sqrt{\dfrac{15}{4}}}{2}\)

\( (x - 1= \dfrac{-1}{2} , -4) ~or~ x - 1 = \dfrac{ \dfrac{1}{2} \pm i\sqrt{\dfrac{15}{4}}}{2}\)

\( x = \dfrac{1}{2} , -3 , \dfrac{3 \pm i\sqrt{15}}{4}\)

Log in to reply

I expanded it, and by hit and trial method, -1 was the solution. Then I divided the expanded polynomial by (x+1). The resultant cubic can be easily factorised.

Log in to reply

x= -1 or 1/2

Log in to reply

Can I know how to solve this, please?

Log in to reply

What have you tried?

Do you know how to clear denominators and factorize?

Log in to reply

\(4x^2\) - \(8x^3\) + \(3x^2\) + \(10x\) - \(5\) = \(0\)

What to do next?

Log in to reply

rational root theorem

well, we want to start to factorize the polynomial. You can use theto guess at possible roots, and after which use the remainder factor theorem to help factorize. Have you seen these theorems before?

Log in to reply

Log in to reply