If a and b are the minimum and maximum of x satisfying 5 + 12/(x + 1/x) = 10, select the correct statements from the following:

1.5a + 5b = 12

2.0 < (b - a) < 1/2

3.A < 0 < b

4.A < 1 < b

5.(b - a)^2 + 6/25 = 2

A1, 2 only

B1, 3 only

C1, 4 only

D1, 4, 5 only ✓ Correct

Correct answer: (D) 1, 4, 5 only

Explanation

Statements 1, 4 and 5 are correct.

5 + 12/(x + 1/x) = 10 gives x + 1/x = 12/5, so x^2 - 2.4x + 1 = 0.

Sum of roots a + b = 2.4, so 5a + 5b = 5 * 2.4 = 12 (Statement 1).

Roots are 0.537 and 1.863, so a < 1 < b holds (Statement 4).

(b - a)^2 = discriminant = 44/25, and 44/25 + 6/25 = 2 (Statement 5).

Want more like this? Create a free account to practise a full test, track your progress, and get spaced-repetition review.