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Algebra Level 5

If a − b a + b a − b ⋯ = a − 3 4 b 2 − 1 2 b \sqrt{a-b\sqrt{a+b\sqrt{a-b\sqrt {\cdots}}}}=\sqrt{a-\dfrac{3}{4}b^2}-\frac{1}{2}b then:

b 2 = a b^2=a none of these choices a > b 2 a>b^2 b 2 ≥ a b^2\geq a a < b a<b

Atul Shivam by Atul Shivam , 23, India

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1 solution

Aman Dubey
Apr 11, 2016

As LHS is in roots so RHS must be greater than zero

⇒ a − 3 4 b 2 − 1 2 b > = 0 \Rightarrow \sqrt{a - \frac {3}{4}b^2} - \frac {1}{2}b >= 0 On solving this we get a > b 2 a > b^2

1 Helpful 0 Interesting 0 Brilliant 0 Confused

nice approach....

Atul Shivam - 5 years, 2 months ago

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