Solve system of equations: x^(1/2) + y=11, x+ y^(1/2)=9 (random fun)

[ffardeen]

My maths teacher challenged me to solve the following for exact values of x and y. Its actually not that straight forward. I used online calculators but they give complex decimal numbers.

x^(1/2) + y=11
x+ y^(1/2)=9

 

[Deleted member 4993]

My maths teacher challenged me to solve the following for exact values of x and y. Its actually not that straight forward. I used online calculators but they give complex decimal numbers.

x^(1/2) + y=11
x+ y^(1/2)=9

If I were to do this problem, I would first substitute:

x^(1/2) = u ............. and y^(1/2)=v

Then we have:

u + v^2 =11

u^2 + v = 9

Then:

11 - u = (9 - u^2)^2

Now you have one equation with one unknown - continue....

 

[stapel]

My maths teacher challenged me to solve the following for exact values of x and y. Its actually not that straight forward. I used online calculators but they give complex decimal numbers.

x^(1/2) + y=11
x+ y^(1/2)=9

Since your instructor challenged you to solve this, then let's see what you've tried so far! You've learned about substitution, so which variable did you pick, in which equation? How did you plug this into the other equation? Where are you getting stuck?

Please be complete. Thank you!