Multiple choice

Directions: In each of the following question two equation are given. Solve the equation are given answer. I. 8x2 - 78x + 169 = 0 II. 20y2 - 117y + 169 = 0

  1. If x<y

  2. If x<=y

  3. If x>y

  4. If x>=y

  5. x=y or relationship between x and y cannot be established
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Solving 8x^2 - 78x + 169 = 0 gives x = 6.5, 3.25. Solving 20y^2 - 117y + 169 = 0 gives y = 3.25, 2.6. Comparing values, x >= y.

AI explanation

For the first equation 8x2 - 78x + 169 = 0, splitting the middle term gives (2x - 13)(4x - 13) = 0, which yields x = 6.5 or x = 3.25. For the second equation 20y2 - 117y + 169 = 0, splitting the middle term gives (4y - 13)(5y - 13) = 0, which yields y = 3.25 or y = 2.6. Comparing these values, the lowest value of x (3.25) is equal to the highest value of y (3.25), and the highest value of x (6.5) is greater than all values of y. Since every value of x is either greater than or equal to every corresponding value of y, the result is x ≥ y.

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