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 September 28th, 2016, 12:56 AM #1 Senior Member   Joined: Jul 2011 Posts: 405 Thanks: 16 real values of a if $\sin x+\cos x= y^2-y+a$ the equation has no real values of $x$ for any real values of $y,$Then values of $a$ September 28th, 2016, 07:39 AM #2 Senior Member   Joined: Sep 2015 From: USA Posts: 2,552 Thanks: 1402 show some work Thanks from panky September 28th, 2016, 02:42 PM #3 Global Moderator   Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,963 Thanks: 1148 Math Focus: Elementary mathematics and beyond $\displaystyle a\gt\sqrt2+\frac14$ Thanks from panky and topsquark September 29th, 2016, 01:05 AM #4 Senior Member   Joined: Jul 2011 Posts: 405 Thanks: 16 Using greg 1313 hint $-\sqrt{2} \leq \sin x+\cos x \leq \sqrt{2}\;\forall x\in \mathbb{R}$ So $\displaystyle \underbrace{\sin x+\cos x}_{\bf{\leq \sqrt{2}}} = y^2-y+\frac{1}{4}+a-\frac{1}{4} = \left(y-\frac{1}{2}\right)^2+a-\frac{1}{4}$ So $\displaystyle a-\frac{1}{4}>\sqrt{2}$ for no real solution. So we get $\displaystyle a>\sqrt{2}+\frac{1}{4}$ Tags real, values 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 panky Algebra 2 May 26th, 2016 02:31 AM RKJCHENNAI Abstract Algebra 2 February 20th, 2016 03:25 AM xamdarb Calculus 2 March 14th, 2014 06:34 PM Punch Algebra 7 June 15th, 2012 05:00 AM kevpb Algebra 3 May 23rd, 2012 09:29 PM

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