The roots of the equation 2√x+2x^-(1)/(2)=5 can be found by solving:

1954 AMC 12 Problem 21

Attempt Problem 21 of the 1954 AMC 12 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1954 AMC 12 solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

21.

The roots of the equation

2\sqrt{x}+2x^{-\frac{1}{2}}=5

can be found by solving:

16x^2-92x+1=0

4x^2-25x+4=0

4x^2-17x+4=0

2x^2-21x+2=0

4x^2-25x-4=0

Multiply by

\sqrt{x}

to remove the negative exponent

Isolate the radical in

2x+2=5\sqrt{x}

before squaring

Multiplying by

\sqrt{x}

gives

2x+2=5\sqrt{x}.

Squaring and simplifying,

4x^2+8x+4=25x,

4x^2-17x+4=0.

Thus, the correct answer is C.