Algebra Problem

Solve equation below:

\[ \displaystyle a \sin |2z| + \log_5 (x \sqrt[8]{2 - 5x^8}) + a^2 = 0 \]

((y2−1)cos⁡2z−ysin⁡2z+1)(1+π+2z+π−2z)=0 \displaystyle ((y^2 - 1) \cos^2 z - y \sin 2z + 1)(1 + \sqrt{\pi + 2z} + \sqrt{\pi - 2z}) = 0

#Algebra #MathProblem #Math

Note by Fariz Azmi Pratama
7 years, 6 months ago

No vote yet
8 votes

  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:

  • Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused .
  • Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting "I don't understand!" doesn't help anyone.
  • Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.
  • Stay on topic — we're all here to learn more about math and science, not to hear about your favorite get-rich-quick scheme or current world events.

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold

- bulleted
- list
  • bulleted
  • list

1. numbered
2. list
  1. numbered
  2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1

paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)example link
> This is a quote
This is a quote
    # I indented these lines
    # 4 spaces, and now they show
    # up as a code block.

    print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears as
Remember to wrap math in \( ... \) or \[ ... \] to ensure proper formatting.
2 \times 3 2×3 2 \times 3
2^{34} 234 2^{34}
a_{i-1} ai−1 a_{i-1}
\frac{2}{3} 23 \frac{2}{3}
\sqrt{2} 2 \sqrt{2}
\sum_{i=1}^3 ∑i=13 \sum_{i=1}^3
\sin \theta sin⁡θ \sin \theta
\boxed{123} 123 \boxed{123}

Comments

This Solution Only for Real Solution\textbf{This Solution Only for Real Solution}

Suppose that:

log⁡5(x(2−5x88=t\displaystyle \log_{5} (x(\sqrt[8]{2-5x^8}=t

sin⁡∣2z∣=q\sin |2z|=q

Obtained

a2+aq+t=0a^2+aq+t=0

Using formula abcabc obtained:

a=−q+q2−4t2\displaystyle a=\frac{-q+\sqrt{q^2-4t}}{2}

Or:

a=−q−q2−4t2\displaystyle a=\frac{-q-\sqrt{q^2-4t}}{2}

From:

http://www.wolframalpha.com/input/?i=y%3Dlog_5%28%28x^8+%282-5x^8%29%29^%281%2F8%29%29

tmax=−18t_{max}=-\frac{1}{8}

Now, check maximum qq

From equation 22 are obtained

1. −pi2≤z≤pi2\frac{-pi}{2} \leq z \leq \frac{pi}{2}

2. (y2−1)cos⁡2z−ysin⁡2z+1=0(y^2-1)\cos^2 z-y\sin 2z+1=0

ycos⁡z=sinzy \cos z=sin z

tan⁡z=y\tan z= y,

so we obtain solution y=tan⁡zy=\tan z, where ∣z∣≤π2|z| \leq \frac {\pi}{2}

Now, for real solution:

froma2+qa+ta^2+qa+t first equation we obtain:

D≥0D \geq 0

q2−4t≥0q^2-4t \geq 0

And we get maksimum t=−18t=\frac {-1}{8} from wolframalfa

So,

q2−4tq^2-4t, always definit positif for 0<x<(25)80<x < \sqrt[8]{\left ({\frac{2}{5}} \right) }

Solution:

y=tan⁡zy=\tan z

−π2≤z≤π2 -\frac{\pi}{2} \leq z \leq \frac{\pi}{2}

0<x<(25)80<x < \sqrt[8]{\left ({\frac{2}{5}} \right) }

And

root of

a2+aq+t=0a^2+aq+t=0

I think it’s not closed problem\textbf{I think it's not closed problem}

:)

pebrudal zanu - 7 years, 6 months ago

Hmmmm...

pebrudal zanu - 7 years, 6 months ago

Log in to reply

That's an ugly equation!

Mark Mottian - 7 years, 6 months ago

Log in to reply

Yes, I think like that... very ugly :(

pebrudal zanu - 7 years, 6 months ago
×

Problem Loading...

Note Loading...

Set Loading...