Melody

the general term is

\(T_n=\binom {9}{n} \left(\frac{5}{x}\right)^n(x^{0.5})^{9-n}\\ T_n=\binom {9}{n} (5^n)(x^{-n})(x^{4.5-0.5n})\\ T_n=\binom {9}{n} (5^n)(x^{4.5-1.5n})\\ \text{for the constant term} \quad \\ 4.5-1.5n=0\\ 9-3n=0\\ 3n=9\\ n=3\\ T_3=\binom {9}{3} (5^3)\\ T_3=84 *125\\ T_3=10500 \)

You need to check this.

Coding:

T_n=\binom {9}{n} \left(\frac{5}{x}\right)^n(x^{0.5})^{9-n}\\
T_n=\binom {9}{n} (5^n)(x^{-n})(x^{4.5-0.5n})\\
T_n=\binom {9}{n} (5^n)(x^{4.5-1.5n})\\
\text{for the constant term}  \quad \\
4.5-1.5n=0\\
9-3n=0\\
3n=9\\
n=3\\
T_3=\binom {9}{3} (5^3)\\
T_3=84 *125\\
T_3=10500
 

\(z\bar{z}^3+\bar{z}z^3=350\\ (a+bi)(a-bi)^3+(a-bi)(a+bi)^3=350\\ (a^2-(bi)^2)[(a-bi)^2+(a+bi)^2]=350\\ (a^2+b^2)[(a^2-2abi-b^2)+(a^2+2abi-b^2)]=350\\ (a^2+b^2)[(2a^2-2b^2)]=350\\ (a^2+b^2)(a^2-b^2)=175\\ a^4-b^4=175 \)

So the solution are   (

\(z=+4\pm3i\\ z=-4\pm3i\)

So assuming i have made no silly mistakes the area is 48 units squared

coding:

z\bar{z}^3+\bar{z}z^3=350\\
(a+bi)(a-bi)^3+(a-bi)(a+bi)^3=350\\
(a^2-(bi)^2)[(a-bi)^2+(a+bi)^2]=350\\
(a^2+b^2)[(a^2-2abi-b^2)+(a^2+2abi-b^2)]=350\\
(a^2+b^2)[(2a^2-2b^2)]=350\\
(a^2+b^2)(a^2-b^2)=175\\
a^4-b^4=175

15*6*8*3!

ok, next time give your reason right from the beginining.

Don't vote people down. Thank them for their interest in you question, explain why you think they are incorrect.

Then maybe you will learn together when someone else answers.

If you are both members you could even become friends.

Maybe you have an adblocker that you do not know about ?

If you are not sure maybe one of our other users can help you find out. 

I can't, I do not know about such things. 

But I am sure others would be able to .

Why do you think your rebuke is worth 3 points NewMember? 

I think it is worth -3 points. 

Behave yourself and say thanks for the person's interest before you suggest that an anwer is wrong.

AND

If you believe an answer is wrong then you are expected to say why you know this to be true. 

  e.g. the answer in the book is ..... 

Attn:   NewMember.

You ask four questions all at once which automatically means you are using this site as a cheat site.

You give yourself as many points as is humanly possible. (it is in really bad taste to give yourself points for posting questions)

You criticize other people when you do not like their answers.

You take points off people at the drop of a hat.

And you never say thank you to anyone!

Your saving graces are that you do answer some questions

And the questions that you do ask are at least interesting. (Even though we are doing your homework for you.)

Please start improving your attitude !

There is a lot of work in that solution Omi.

Your geometry answers are masterpieces! 

I just added tihs  question and answer to our list in the Feature questions sticky topics.      

Heureka fas provided a insight into this question that I really like.

Thanks Heureka!