Multiple choice

Directions: In each of these questions, two equations (I) and (II) are given. You have to solve both the equations and give answer. I. 11x + 64/x = 54 II. 12y2 + 40y + 17 = 0

  1. x > y

  2. x ≤ y

  3. x ≥ y

  4. x < y

  5. x = y or relationship between x and y can't be established
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A Correct answer
Explanation

I: 11x + 64/x = 54 => 11x^2 - 54x + 64 = 0. Roots are x = 4 and x = 16/11 (approx 1.45). II: 12y^2 + 40y + 17 = 0. Roots are y = -0.5 and y = -2.83. Since both roots of x are positive and both roots of y are negative, x > y.

AI explanation

Multiply equation I by x to form the quadratic equation 11x^2 - 54x + 64 = 0, then use the factorization method to split the middle term into -22x and -32x to get (11x - 32)(x - 2) = 0. The roots for x are 32/11 and 2. For equation II, use the factorization method to split the middle term of 12y^2 + 40y + 17 = 0 into 6y and 34y, yielding (6y + 17)(2y + 1) = 0, which gives the roots y = -17/6 and y = -1/2. Since the smallest value of x is 2 and the largest value of y is -1/2, x > y.

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