Solve 2x-x1/2-1=0 using the cuadratic formula?

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Answer 1 · 2018-01-28T10:11:11

#x=1#. See explanation.

Given #2x-x^(1/2)-1=0#, let #u = x^(1/2)# and the equation becomes:

#2u^2 -u - 1 =0#

Using the quadratic formula on this we have:

#u=(-(-1) pm sqrt((-1)^2-4(2)(-1)))/(2(2))#

#u=(1 pm sqrt(1+8))/(4)#

#u=(1 pm 3)/(4)#

So, #u = 1# or #u=-1/2#, where #u=x^(1/2)#, which means:

#x^(1/2)=1 rarr x =1#

#x^(1/2) ne -1/2# (think of the range of #x^(1/2)#)

So the only solution is #x=1#.