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


3 years ago

Shailendra Kumar Sharma
188 Points
							given condition is that(A+B)/2 = 2$\sqrt{AB}$ $(A+B)/\sqrt{AB}$  =4Applying 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)

3 years ago
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• 101 Video Lectures
• Revision Notes
• Test paper with Video Solution
• Mind Map
• Study Planner
• NCERT Solutions
• Discussion Forum
• Previous Year Exam Questions