2^(2x^2 +1) - 9*2^(x^2 +x) + 2^(2x +2) =0 Giúp mình vs ạ
1 câu trả lời
$2^{(2x^2 +1)} - 9.2^{(x^2 +x)} + 2^{(2x +2)} =0$
⇔$2.(2^{x^2})^2-9.2^{x^2}.2^x+4.(2^x)^2=0$
Đặt $2^{x^2}=a ; 2^x=b $ (a;b>0)
Pt⇔ $2a^2-9ab+4b^2=0$
⇔$(2a-b)(a-4b)=0$
⇔\(\left[ \begin{array}{l}a=b/2\\a=4b\end{array} \right.\)
⇔\(\left[ \begin{array}{l}2^{x^2}=2^x /2=2^{x-1}\\2^{x^2}=4.2^x=2^{x+2}\end{array} \right.\)
⇔\(\left[ \begin{array}{l}x^2=x-1\\x^2=x+2\end{array} \right.\)
⇔\(\left[ \begin{array}{l}x=2\\x=-1\end{array} \right.\)
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