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 May 14th, 2012, 11:10 PM #1 Member   Joined: Apr 2012 Posts: 72 Thanks: 3 find x ?( (1-?(1-x^2))/2 ) + ?( (1+?(1-x^2))/2 ) = ?(1+x) May 15th, 2012, 12:09 AM #2 Senior Member   Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs Re: find x We are given: We see we require in order for the left side to represent real values. Multiply through by : Square both sides since they are non-negative: Case 1: Hence, we find: Case 2: No solution for this case, thus we are left with: May 15th, 2012, 12:35 AM #3 Member   Joined: Apr 2012 Posts: 72 Thanks: 3 Re: find x Thanks a lot! May 15th, 2012, 06:13 AM #4 Math Team   Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1038 Re: find x A sorta "short cut to typing!" I'd use here: since x^2 - 1 = (x+1)(x-1): let a = x+1 and b = x-1; so, after multiplication by SQRT(2), you have: SQRT[1 - SQRT(ab)] + SQRT[1 + SQRT(ab)] = SQRT(2a) Easier to do the squaring both sides et al... I'm lazy  May 15th, 2012, 09:55 AM #5 Global Moderator   Joined: Dec 2006 Posts: 20,942 Thanks: 2210 Assuming |x| ? 1, let x = sin(2A), where |2A| ? ?/2, and recall that cos(2A) = 2cos�(A) - 1 = 1 - 2sin�(A). The equation becomes |sin(A)| + |cos(A)| = ?(1 + sin(2A)). Squaring gives 1 + |sin(2A)| = 1 + sin(2A), i.e. |x| = x, so 0 ? x ? 1. Tags find Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post kingkos Algebra 5 November 24th, 2012 11:40 PM kevinman Algebra 8 March 8th, 2012 05:53 AM

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