+118658 \(x ^ {0.5} + x^2 = 17\\ x ^ {0.5} + (x ^ {0.5} )^4 = 17\\ let\;\;t=x ^ {0.5} \\ t+t^4=17\\ t^4+t-17=0 \)
This has at most 4 real answers.
If I graph \(y=x^4+x-17\)
and see where it crosses the x axis that will be the solutions.
So t might equal 1.969 or -2.09
\(t=x^{0.5}\\ t^2=x\\ If\;\;t=1.969,\quad x=3.877\\ LHS=3.877^{0.5}+3.877^2=21.2\ne RHS\\~ \\If\;\;t=-2.09,\quad x=4.368\\ LHS=4.368^{0.5}+4.368^2=17=RHS\\~\)
So I get x= 3.877 Correct to 3 decimal places
I am going to enter this into WolframAlpha to see if our answers are the same.
https://www.wolframalpha.com/input/?i=x%5E+0.5+%2B+x%5E2+%3D+17
Our answers are the same.
