# 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, 12 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

- 4 years, 12 months ago

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

- 4 years, 12 months ago

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

- 4 years, 12 months ago

no problem :)

- 4 years, 12 months ago

Thanks guys! :)

- 4 years, 12 months ago

is this a question in a Philippine Math Olympiad?

- 4 years, 12 months ago

Yes! :) On the QS.

- 4 years, 12 months ago

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

- 4 years, 12 months ago

- 4 years, 12 months ago

x<=-2

- 4 years, 12 months ago