Question

Apartine multimii???????

Answer 1

fie 2^x=t
atunci
4^x=t²
si expresia devine
t²+1/t²=23
t²+1/t²+2=23+2
t²+1/t²+2*t*1/t=25
(t+1/t)²=25
t+1/t∈{-5;5} varianta a)

Answer 2

[tex]\it 4^x+4^{-x} =23\ \ \ \ (*) \\ \\ (2^x+2^{-x})^2 = 2^{2x} + 2\cdot2^x\cdot2^{-x} +2^{-2x} = 4^x+2^{1+x-x} +\dfrac{1}{2^{2x}} = \\ \\ \\ = 4^x+2+\dfrac{1}{4^x} = 4^x+4^{-x} +2\ \stackrel{(*)}{=}\ 23+2 = 25 \Longrightarrow \\ \\ \\ \Longrightarrow \sqrt{(2^x + 2^{-x})^2} = \sqrt{25} \Longrightarrow 2^x+2^{-x} = 5[/tex]