Question

If (x + 1) ∶ (x + 5) ∶∶ (x + 17) ∶ (x + 53) then what is the mean proportional between (x + 5) and (9x – 1) where x > 0?

• A. $$10\sqrt{2}$$
• B. $$3\sqrt{2}$$
• C. $$4\sqrt{13}$$
• D. $$4\sqrt{3}$$

Answer 1

Answer:

$$4\sqrt{3}$$

Solution: Given: (x + 1) ∶ (x + 5) ∶∶ (x + 17) ∶ (x + 53) Concept used: Mean proportion of two numbers x and y = √(x × y) Calculation: Here, (x + 1)/(x + 5) = (x + 17)/(x + 53) ⇒ x2 + 53x + x + 53 = x2 + 17x + 5x + 85 ⇒ x2 + 53x + x - x2 - 17x - 5x = 85 - 53 ⇒ 32x = 32 ⇒ x = 32/32 ⇒ x = 1 Now, (x + 5) and (9x – 1) = (1 + 5), (9 × 1 - 1) ⇒ 6, 8 Now, mean proportion = √(6 × 8) ⇒ √48 ⇒ 4√3 ∴ Required mean proportion is 4√3.