4^х+1 - 6^х ≥ 2 * 3^2х+2<br />2^2(х+1) - 2^х *3^x≥ 2 * 3^2(х+1)<br />4*2^2х - 2^х *3^x≥ 18 * 3^2х<br />разделим все на 3^2х<br />4*(2/3)^2х - (2/3)^х ≥ 18<br />заменим y=(2/3)^х<br />4y²-y-18≥0<br />D=1+4*4*18=289<br />√D=17<br />y1=(1-17)/8=-2<br />у2=(1+17)/8=18/8=9/4<br />(у+2)(у-9/4)≥0 <br /> у принадлежит интервалу (-∞,-2]и[9/4;+∞) <br /> вспоминаем, что у должен быть >0 по определению, так как стереть положительного числа всегда положительна. <br /> Поэтому у принадлежит [9/4;+∞) <br /> (2/3)^х=9/4<br />(2/3)^х=(3/2)^2<br />(2/3)^х=(2/3)^(-2)<br /> ответ х принадлежит интервалу [-2;+∞) или иначе говоря х≥-2
I think summer is the best season of all because it is warm, the nature is beautiful and we have great opportunities for rest. Summer is a time of holidays. We can go anywhere, spend our time near a river or a lake on fresh, green grass, swim in warm water, or climb mountains, play different games, ride a bicycle and so on.I spend my summer holidays at my granny’s. There are many things there to do. What I did most of the time - I swam in the sea and sunbathed. Sometimes I made a fire with my friends at the seaside and cooked potatoes there. It was wonderful. We told anecdotes to each other, and did everything we wanted. I also got used to walk alone in the forest.When August was coming to its end, I went on a small voyage by ship. The ship name was “Sevastopol”.But this summer wasn’t for me only sugar and honey. I have passed through the graduating exams after school and entering exams in the university. So the bigger part of my summer vacations I spent sitting with the books. Of course, it was not interesting, but I’m glad that I did it because now I’m a student of the best university in our country.
