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Inequality Problem

What is the solution set of the inequality \[\left ( \frac{\pi}{2} \right )^{(x-1)^2}\leq \left ( \frac{2}{\pi} \right )^{x^2-5x-5}?\]

Note by John Marvin Macaraeg
4 years, 2 months ago

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(pi/2)^(x^2-2x+1) < (pi/2)^(5x+5-x^2) We apply the natural Log funtion (x^2-2x+1) * ln(pi/2) < (5x+5-x^2) * ln(pi/2) x^2-2x+1<5x+5-x^2 2x^2-7x-4<0 2(x-4)(x+1/2)<0 [-1/2,4] I forgot the equal sign Ahmed Taha · 4 years, 2 months ago

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@Ahmed Taha a little more space b/w the letters will make this soln. perfect.....:) Riya Gupta · 4 years, 2 months ago

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@Riya Gupta Sorry for that, I am new to tying here :) Ahmed Taha · 4 years, 2 months ago

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@Ahmed Taha no problem :) Riya Gupta · 4 years, 2 months ago

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Thanks guys! :) John Marvin Macaraeg · 4 years, 2 months ago

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is this a question in a Philippine Math Olympiad? Christian Baldo · 4 years, 2 months ago

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@Christian Baldo Yes! :) On the QS. John Marvin Macaraeg · 4 years, 2 months ago

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[-1/2,4] You should be able to work out how I got this. HINT: what can you do since the bases are reciprocals? Bob Krueger · 4 years, 2 months ago

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@Bob Krueger yeah...answer...[-1/2,4]...agreed...:) Riya Gupta · 4 years, 2 months ago

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x<=-2 Nagendra Y · 4 years, 2 months ago

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