SOLUTION: solve for x: x^(1/2) + 4x^(-1/2)=5 please and thank you

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Question 937567: solve for x: x^(1/2) + 4x^(-1/2)=5
please and thank you
Found 2 solutions by MathLover1, MathTherapy:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

x%5E%281%2F2%29+%2B+4x%5E%28-1%2F2%29=5
sqrt%28x%29+%2B+4%2Fsqrt%28x%29=5
%28sqrt%28x%29%2Asqrt%28x%29%29%2Fsqrt%28x%29+%2B+4%2Fsqrt%28x%29=5
%28sqrt%28x%29%29%5E2%2Fsqrt%28x%29+%2B+4%2Fsqrt%28x%29=5
x%2Fsqrt%28x%29+%2B+4%2Fsqrt%28x%29=5
%28x+%2B+4%29%2Fsqrt%28x%29=5

%28x+%2B+4%29=5%2A5sqrt%28x%29 .............square both sides

%28x+%2B+4%29%5E2=%285sqrt%28x%29%29%5E2
x%5E2%2B8x+%2B+16=25x
x%5E2-25x%2B8x+%2B+16=0

x%5E2-17x+%2B+16=0
x%5E2-1x-16x+%2B+16=0
%28x%5E2-1x%29-%2816x-+16%29=0
x%28x-1%29-16%28x-+1%29=0
%28x-16%29+%28x-1%29+=+0

solutions:
x-16=0 => x=16
and
x-1=0 => x=1











Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

solve for x: x^(1/2) + 4x^(-1/2)=5
please and thank you
highlight%28highlight%28x%5E%281%2F2%29+%2B+4x%5E%28-1%2F2%29+=+5%29%29

highlight%28sqrt%28x%29+%2B+4%2Fx%5E%281%2F2%29+=+5%29

sqrt%28x%29+%2B+4%2Fsqrt%28x%29+=+5

%28sqrt%28x%29%29%5E2+%2B+4+=+5sqrt%28x%29  ------ Multiplying by LCD, sqrt%28x%29

x+%2B+4+=+5sqrt%28x%29

sqrt%28x%29+=+%28x+%2B+4%29%2F5

%28sqrt%28x%29%29%5E2+=+%28%28x+%2B+4%29%2F5%29%5E2 ------ Squaring each side

x+=+%28x%5E2+%2B+8x+%2B+16%29%2F25

x%5E2+%2B+8x+%2B+16+=+25x ------- Cross-multiplying

x%5E2+%2B+8x+-+25x+%2B+16+=+0%7D%7D%0D%0A%7B%7B%7Bx%5E2+%96+17x+%2B+16+=+0

x%5E2+-+17x+%2B+16+=+0

(x - 16)(x - 1) = 0 

highlight_green%28system%28x+=+16_or%2Cx+=+1%29%29

You can do the check!!