Question

cine mă ajută și pe mine?​

Answer 1

Răspuns:

Explicație pas cu pas:

Answer 2

$\it 7^{x^2-x}=7^{5x-x}\ \Rightarrow\ x^2-x=5x-x\ \Rightarrow\ x(x-1)=5(x-1)\ \Rightarrow\\ \\ \ \Rightarrow\ \ x(x-1)-5(x-1)=0\ \Rightarrow\ (x-1)(x-5)=0\ \Rightarrow\ x_1=1,\ \ x_2=5\\ \rule{190}{0.5}\\ \\ 2^{x-1}+2^x=12|_{\cdot2}\ \Rightarrow\ 2^x+2\cdot2^x=24\ \Rightarrow\ 3\cdot2^x=24|_{:3}\ \Rightarrow\ 2^x=8\ \Rightarrow\ x=3\\ \\ \rule{200}{0.6}\\ \\ \sqrt{x^2-4}+\sqrt{x-2}=0\ \Rightarrow\ \sqrt{(x-2)(x+2)}+\sqrt{x-2}=0\ \Rightarrow$

$\it \Rightarrow\ \sqrt{x-2}\cdot\sqrt{x+2}+\sqrt{x-2}=0 \Rightarrow\ \sqrt{x-2}(\underbrace{\sqrt{x+2}+1}_{>0})=0 \Rightarrow\ x=2$

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$\it lg^2x-5lgx+6=0\\ \\ Vom\ \ nota\ \ lgx=t,\ iar\ ecua\c{\it t}ia\ \ devine:\\ \\ t^2-5t+6=0\ \Rightarrow\ t^2-2t-3t+6=0\ \Rightarrow\ t(t-2)-3(t-2)=0\ \Rightarrow\ \\ \\ \ \Rightarrow\ (t-2)(t-3)=0\ \Rightarrow\ t\in\{2,\ \ 3\}\\ \\ t=2\ \Rightarrow\ lgx=2\ \Rightarrow\ x=10^2=100\\ \\ t=3\ \Rightarrow\ lgx=3\ \Rightarrow\ x=10^3=1000$