Expo-equation

May 2009
596
31
ALGERIA
Solve in R:
\(\displaystyle
x^{2}\times 2^{\sqrt{2x+1}-1}+2^{x}=2^{\sqrt{2x+1}+1}+x^{2}\times 2^{x-2}
\)
 
  • Like
Reactions: Amer
May 2009
1,096
396
Jordan
Solve in R:
\(\displaystyle
x^{2}\times 2^{\sqrt{2x+1}-1}+2^{x}=2^{\sqrt{2x+1}+1}+x^{2}\times 2^{x-2}
\)
\(\displaystyle 2^{\sqrt{2x+1}-1} = 2^{x-2} \)

and find x
 

Grandad

MHF Hall of Honor
Dec 2008
2,570
1,416
South Coast of England
Hello everyone
\(\displaystyle 2^{\sqrt{2x+1}-1} = 2^{x-2} \)

and find x
This only gives the solution \(\displaystyle x = 4\) (which is correct), but there is also a solution at \(\displaystyle x = 2\). I think you'll have to replace the \(\displaystyle x^2\) terms by an expression in the form \(\displaystyle x = 2^y\) and the compare coefficients to get this solution.

Grandad