Solve: x^(1/2)+x^(1/4)=10?

Question

Please help!!!!!!!!!!!!!!!!!!!!!!!!

Answer 1

x^( 1/2) + x^( 1/4) =10--------1

subtract x^( 1/2) from each side

          x^( 1/4) =10 -x^1/2---------2

equation 2 each side squaring

         x^( 1/4)^2 =(10 -x^1/2)^2

        x^1/2  = 100 + x - 20 x^1/2

add 20 x^1/2 from each side

  21x^1/2  = 100 + x-----------3

equation 3 each side squaring

       441x = 10000 +x^2 + 200x

      x^2 -241x +10000=0

comparing the equation ax^2 +bx +c

 a =1 , b = -241 ,c =10000

the formula is   = (- b±sqrt( b^2 -4ac)) /2a

                     =(241±sqrt( 241^2 -4*1*10000)) /2

                     =(241±sqrt(58081 -40000))/2

                   =(241±sqrt(18081)) /2

the solution is ( 241 +sqrt(18081))/2  ,( 241 -sqrt(18081))/2

Answer 2

Let us assume that x^1/4 = y.

Therefore .

Check:

Therefore is a solution.

Therefore is not a solution.

Therefore the solution is .