Multiple choice

The roots of the equation 6x3/4 = 7x1/4 - 2x-1/4 are

  1. 4/9 and 1/9

  2. 9/4 and 1/4

  3. 4/9 and 1/4

  4. None of these
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C Correct answer
AI explanation

Multiply the equation 6x3/4 = 7x1/4 - 2x-1/4 by x1/4 to clear the negative exponent, yielding 6x = 7x1/2 - 2. Substitute y equal to x1/2, which changes the equation to 6y2 - 7y + 2 = 0. Factoring this quadratic gives (3y - 2)(2y - 1) = 0, revealing y equal to 2/3 and 1/2. Squaring these values gives the roots x equal to 4/9 and 1/4.

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