Question

9sqrt(x) + 40 ^ sqrt(x) = 41 ^ sqrt(x)

Answer 1

Answer:

√x+40-√x = 4

Step by step solution :

STEP1:Isolate a square root on the left hand side

     Original equation

     √x+40-√x = 4

     Isolate

     √x+40 = √x+4

STEP2:Eliminate the radical on the left hand side

     Raise both sides to the second power

     (√x+40)2 = (√x+4)2

     After squaring

     x+40 = x+16+8√x

STEP3:Get remaining radical by itself

     Current equation

     x+40 = x+16+8√x

     Isolate radical on the left hand side

     -8√x = -x-40+x+16

      Tidy up

     8√x = 24

STEP4:Eliminate the radical on the left hand side

     Raise both sides to the second power

     (8√x)2 = (24)2

     After squaring

     64x = 576

STEP5:Solve the linear equation

     Rearranged equation

      64x  -576 = 0

     Add  576  to both sides

      64x  = 576

     Divide both sides by 64

     A possible solution is :

     x = 9

STEP6:Check that the solution is correct

     Original equation, root isolated, after tidy up

     √x+40 = √x+4

     Plug in 9 for  x 

      √(9)+40 = √(9)+4

      Simplify

      √49 = 7

      Solution checks !!

     Solution is:

      x = 9

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