Question

Rezolvati in R inecuatiile: 2(x+radical din 2) -radical din 50 < radical din 2(2x-3)-4
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Answer 1

2(x+radical din 2) -radical din 50 < radical din 2(2x-3)-4

2(x + √2) - √(50) <  √2(2x - 3) - 4

$\it \sqrt{50}=\sqrt{25\cdot2}=5\sqrt2\\ \\ 2(x+\sqrt2)-5\sqrt2<\sqrt2(2x-3)-4 \Rightarrow 2x+2\sqrt2-5\sqrt2<2\sqrt2x-3\sqrt2-4 \Rightarrow\\ \\ 2x-2\sqrt2x<-3\sqrt2-4-2\sqrt2+5\sqrt2 \Rightarrow 2x(1-\sqrt2)<-4|_{:2} \Rightarrow \\ \\ \Rightarrow x(1-\sqrt2)<-2\Big|_{\cdot(1+\sqrt2)} \Rightarrow x(1-2)<-2(1+\sqrt2) \Rightarrow\\ \\ \Rightarrow-x<-2(1+\sqrt2)|_{\cdot(-1)} \Rightarrow x>2(1+\sqrt2)$