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2 \times 3
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2^{34}
234
a_{i-1}
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\frac{2}{3}
32
\sqrt{2}
2
\sum_{i=1}^3
∑i=13
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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
This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.
When posting on Brilliant:
*italics*or_italics_**bold**or__bold__paragraph 1
paragraph 2
[example link](https://brilliant.org)> This is a quote# I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world"\(...\)or\[...\]to ensure proper formatting.2 \times 32^{34}a_{i-1}\frac{2}{3}\sqrt{2}\sum_{i=1}^3\sin \theta\boxed{123}Comments
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.
x=y+1
(y+1)2+(yy+1)2=45
y2+2y+1+1+y21+y2=45
y2+y21+2y+y2+2=45
a=y+y1
a2−2+2a+2=45
(a+1)2=(±23)2
a=−25,21
y+y1=−25,y+y1=21
y=2−25±49,y=221±i415
x−1=2−25±49,x−1=221±i415
(x−1=2−1,−4) or x−1=221±i415
x=21,−3,43±i15
x= -1 or 1/2
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Can I know how to solve this, please?
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What have you tried?
Do you know how to clear denominators and factorize?
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I've already cleared denominators and got
4x2 - 8x3 + 3x2 + 10x - 5 = 0
What to do next?
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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?
Log in to reply
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!