Multiple choice

In each of these questions, two equations (a) and (b) are given. You have to solve both the equations and choose the correct option.(a) x^2 - 32x + 247 = 0 (b) y^2 - 35y + 304 = 0

  1. $\(x > y\)$
  2. $\(x \le y\)$
  3. $\(x \ge y\)$
  4. $\(x < y\)$

  5. x = y or relationship between x and y can't be established
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

Solving equation (a): x^2-32x+247=0 gives x=(32±√(1024-988))/2=(32±6)/2, so x=19 or x=13. Solving equation (b): y^2-35y+304=0 gives y=(35±√(1225-1216))/2=(35±3)/2, so y=19 or y=16. When x=13, y is always greater. When x=19, x=y when y=19 but x < y when y=19 is false. Actually, when x=19, y can be 16 (so x > y) or 19 (so x = y). Since the relationship varies, it cannot be established consistently. Option E is correct.

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