Question

find the mean proportional to (10+5root3) and (14-7root3)​

Answer 1

Answer:

√35

Step-by-step explanation:

Let the mean proportional is x.

then,

10+5√3 : x = x : 14-7√3

→ $\frac{10+5\sqrt{3} }{x} =\frac{x}{14-7\sqrt{3} }$

→ $x^{2} = (10+5\sqrt{3} )(14-7\sqrt{3} )$

→ x² = 140 - 70√3 + 70√3 - 35×3

→ x² = 35

∴ x = √35