Question

sa se scrie multimile formate cu multimea A,in cazurile: d)A={x€R| 4^x-7×2^x+12=0}​

Answer 1

Răspuns:

Explicație pas cu pas:

$4^{x}-7*2^{x}+12=0\\ 4^{x}=(2^2)^{x}=2^{2x}=> 2^{2x}-7*2^{x}+12=0$

$2^{x}=t,t>0$

$t^{2}-7*t+12=0$

$d=b^{2}-4*a*c=> d=(-7)^{2}-4*1*12=49-48=1$

$t_{1}=\frac{-b+\sqrt{d} }{2*a}=\frac{-(-7)+\sqrt{1} }{2*1}=4>0 \\2^x=4=> 2^x=2^2=>x=2$

$t_{1}=\frac{-b-\sqrt{d} }{2*a}=\frac{-(-7)-\sqrt{1} }{2*1}=3>0$

$2^{x}=3$ => x=㏒₂3

S={2,㏒₂3}