Multiple choice

Directions: In the question, two equations (I) and (II) are given. You have to solve both the equations and give answer. (I) 1 - 17x + 72x2 = 0 (II) 8y + 6 = 5

  1. x > y

  2. x ≥ y

  3. x < y

  4. x ≤ y

  5. x = y or no relation can be established between x and y.
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A Correct answer
Explanation

Eq I: 72x^2 - 17x + 1 = 0. Roots: (8x-1)(9x-1) = 0, so x = 1/8, 1/9. Eq II: 8y = -1, y = -1/8. Since both x values are positive and y is negative, x > y.

AI explanation

Rearranging equation I gives 72x^2 - 17x + 1 = 0, and splitting the middle term yields 72x^2 - 9x - 8x + 1 = 0. Factoring by grouping gives (8x - 1)(9x - 1) = 0, so the roots for x are 1/8 and 1/9. Solving equation II, 8y + 6 = 5 gives 8y = -1, which means y = -1/8. Since both values of x are positive and y is negative, x is always greater than y.

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