Question

The geometric mean proportion between 30 + √200 and 54 - √648 is:
1. 6 \(\sqrt{2}\)
2. 4\(\sqrt{5}\)
3. 6\(\sqrt{35}\)
4. 5\(\sqrt{6}\)

Answer 1

Correct Answer - Option 3 : 6\(\sqrt{35}\)

Calculation:

Let the geometric mean proportion be x.

(30 + √200)/x = x/(54 - √648)

x² = (30 + 10√2) × (54 -18√2)

x2 = 1620 + 540√2 - 540√2 - 360

x2 = √1260 = 6√35.

∴ x  = 6√35.