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. x2 – 13 √2 x + 60 = 0, II. y2 + 3√5 y – 20 = 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
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The roots of the first equation are 10sqrt(2) and 3sqrt(2). The roots of the second are sqrt(5) and -4sqrt(5), and every possible x value is greater than every possible y value, so x > y.

AI explanation

For equation I, the factors are (x - 5 root 2) and (x - 6 root 2), giving x = 5 root 2 and x = 6 root 2. For equation II, the factors are (y + 4 root 5) and (y - root 5), giving y = -4 root 5 and y = root 5. Comparing these values, 5 root 2 is about 7.07 and 6 root 2 is about 8.49, while root 5 is about 2.24, meaning both x values are greater than both y values. Therefore, x > y.

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