Question

Решить, желателен ответ на листке.

Answer 1

$5*4^{x-1}-16^{x}+0,25*2^{2x+2}+7=0\\5*4^{x}*4^{-1}-(4^{x})^{2}+0,25*4^{x}*4+7=0\\1,25*4^{x}-(4^{x})^{2}+4^{x}+7=0\\2,25*4^{x}-(4^{x})^{2}+7=0|*(-4)\\4*(4^{x})^{2}-9*4^{x}-28=0\\4^{x}=m,m>0\\4m^{2}-9m-28=0\\D=9^{2} -4*4*(-28)=81+448=529=23^{2}\\m_{1}=frac{9+23}{8}=4\\m_{2}=frac{9-23}{8}=-frac{14}{8} <0\\4^{x}=4\\x=1$

Answer 2

5•4^(х - 1) - 16^х + 0,25•2^(2х + 2) + 7 = 0
5/4 • 4^х - (4^х)^2 + 0,25•4^(х + 1) + 7 = 0
5/4•4^х - (4^х)^2 + 4^х + 7 = 0
-(4^х)^2 + 9/4 • 4^х + 7 = 0
4•(4^х)^2 - 9•4^х - 28 = 0
4^х = t > 0
4t^2 - 9t - 28 = 0
D = 81 + 16•28 = 81 + 448 = 529
t = (9 (+/-) 23)/8 = {-7/4; 4}
4^х = 4
x = 1