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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, 5 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, 5 months ago

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a little more space b/w the letters will make this soln. perfect.....:)

Riya Gupta - 4 years, 5 months ago

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Sorry for that, I am new to tying here :)

Ahmed Taha - 4 years, 5 months ago

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@Ahmed Taha no problem :)

Riya Gupta - 4 years, 5 months ago

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Thanks guys! :)

John Marvin Macaraeg - 4 years, 5 months ago

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is this a question in a Philippine Math Olympiad?

Christian Baldo - 4 years, 5 months ago

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Yes! :) On the QS.

John Marvin Macaraeg - 4 years, 5 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, 5 months ago

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yeah...answer...[-1/2,4]...agreed...:)

Riya Gupta - 4 years, 5 months ago

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x<=-2

Nagendra Y - 4 years, 5 months ago

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