Solve the equation $3x -7\sqrt x + 2 = 0$
- $-\dfrac {1}{9}$ or $4$
- $\dfrac {1}{9}$ or $-4$
- $-\dfrac {1}{9}$ or $-\dfrac {1}{4}$
- $\dfrac {1}{9}$ or $4$
Reveal answer
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Correct answer
Explanation
Let u = sqrt(x). The equation becomes 3u^2 - 7u + 2 = 0. Factoring gives (3u - 1)(u - 2) = 0. So u = 1/3 or u = 2. Squaring gives x = 1/9 or x = 4.
AI explanation
Substitute t equals the square root of x to convert the equation into a quadratic form 3t squared minus 7t plus 2 equals 0. Factoring this gives (3t minus 1)(t minus 2) equals 0, so t equals one third or t equals 2. Squaring these values gives x equals one ninth or x equals 4.