Question

Find the mean proportional between √11 - √5 and 13√11 + 19√5.

Answer 1

Given:- Find the mean proportional between √11 - √5 and 13√11 + 19√5.⤵

Solution:-⤵

For better answer (answer) see the above photo⤴

Answer 2

Answer:

Let the mean proportional is x.

(√11 - √5): x : : x : (13√11 + 19√5)

x² = (√11 - √5)(13√11 + 19√5)

x² = 13 × 11 + 19√55 - 13√55 - 95

x² = 48 + 6√55

x = √48 + 6√55

x = √48 + 2√9 × 55

x= √33 + √15

Step-by-step explanation:

Hope this helps