Grade 11Algebra

The AM between two positive numbers A and B (A>B) is twice the GM .prove that A:B= 2+√ 3 : 2-√3

Divyansh

8 Years agoGrade 11

8 Years ago

given condition is that
(A+B)/2 = 2 $\sqrt{AB}$

$(A+B)/\sqrt{AB}$ =4
Applying dividendo componendo

$((A+B)+2\sqrt{AB})/(A+B-2\sqrt{AB})=(2+1)/(2-1)$

It can be seen from now

$(\sqrt{A } +\sqrt{B})^{2} /(\sqrt{A } -\sqrt{B})^{2} = 3/1$
Square root both sides

$(\sqrt{A } +\sqrt{B}) /(\sqrt{A } -\sqrt{B}) = \sqrt{3}$
Components dividendo
A/B =(1 +√ 3)/(-√ 3 +1)

algebra

Last Activity: 2 Years ago

algebra

Last Activity: 2 Years ago

algebra

Last Activity: 2 Years ago

algebra

Last Activity: 3 Years ago

algebra

Last Activity: 3 Years ago