Multiple choice

x2 + 2y2 = 1 x = 1/2 Column A Column B |y| 1/2 Compare the two quantities to decide whether

  1. the quantity in Column A is greater

  2. the quantity in Column B is greater

  3. the two quantities are equal

  4. the relationship cannot be determined from the information given
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Given x^2 + 2y^2 = 1 and x = 1/2, then (1/4) + 2y^2 = 1, so 2y^2 = 3/4, y^2 = 3/8. Thus |y| = sqrt(3/8). Since sqrt(3/8) is approximately sqrt(0.375) which is greater than 0.5 (1/2), Column A is greater.

AI explanation

Substituting x = 1/2 into the first equation gives (1/2)^2 + 2y^2 = 1, which simplifies to 2y^2 = 3/4 and y^2 = 3/8. Taking the square root gives |y| = sqrt(3/8), which is approximately 0.612. Comparing this to the value in Column B shows that 0.612 is greater than 0.5. Therefore, the quantity in Column A is greater.

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