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2√ab = (a+b)/2
⇒ 4ab = (a+b)²
⇒ 16ab = a² + b² + ab
⇒ 0 = a² + b² - 14ab
Say, b=1
0 = a² - 14a +1
Then, on solving for a,
a = (14 +√(196 - 4) )/2 or (14 -√(196 - 4 ))/2
= (14 +√(192) )/2 or (14 -√(192 ))/2
= (14 + 8√3)/2 or (14 - 8√3)/2
= 7+ 4√3 or 7- 4√3
⇒a/1 = a/b = 7+ 4√3 or 7- 4√3
Hence, proved.
:)
⇒ 4ab = (a+b)²
⇒ 16ab = a² + b² + ab
⇒ 0 = a² + b² - 14ab
Say, b=1
0 = a² - 14a +1
Then, on solving for a,
a = (14 +√(196 - 4) )/2 or (14 -√(196 - 4 ))/2
= (14 +√(192) )/2 or (14 -√(192 ))/2
= (14 + 8√3)/2 or (14 - 8√3)/2
= 7+ 4√3 or 7- 4√3
⇒a/1 = a/b = 7+ 4√3 or 7- 4√3
Hence, proved.
:)
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