Solve: 3 = x-2√x

leads to
 or 
but only  is viable and it leads to

Solve the equation

7 over 2 x + 1 over 2 x = 3x + 3 over 2 + 5 over 2 x

I believe you are describing: 
 
so that... 




 
 
 

leads to 

 
which has solutions: 

Can you help me solve for real roots? 2x^8+15x^4=27

u=x^4 
2u^2+15u-27=0 
2u^2+18u-3u-27=0 
2u(u+9)-3(u+9)=0 
(2u-3)(u+9)=0 

but u+9 contributes no real roots 

2u-3=0 
u=3/2 

x^4 = 3/2 

x^2 = +- sqrt(3/2) 

from which we use the principal root 

thus 
 
or 

is it possible to write two real numbers whose sum is 4 and whose product is 5?

Your Answer:

this is clearly irreducible...so let's use the quadratic formula...






So, yes if we extend our search out to all real numbers we can find two irrational numbers that meet our requirements

:)

Solve the equation

Solve.

Solution:

Solve the polynomial equation

Solve.