Question

Se dau multimile: A= x€|R | |2x-3| < 7 si B= x€|R | 4x+1>5 PLS DAU COROANA SI 100 PUNCTE !!! EX 4 SI 5 !!!

Answer 1

Răspuns:

Ai răspuns atașat pe foaie.

Answer 2

$\it 4)\ |2x-3|\leq7 \Rightarrow -7 \leq2x-3\leq7|_{+3} \Rightarrow -4\leq2x\leq10|_{:2} \Rightarrow -2\leq x\leq5 \Rightarrow \\ \\ \Rightarrow A=[-2,\ \ 5]\\ \\ \\ 4x+1\geq5|_{-1} \Rightarrow 4x\geq4|_{:4} \Rightarrow x\geq1 \Rightarrow B=[1,\ \infty)\\ \\ A\cup B=[-2,\ \infty);\ \ \ A\cap B=[1,\ \ 5]\\ \\ A\setminus B=[-2,\ \ 1);\ \ \ B\setminus A=(5,\ \infty)$

$\it 5)\ a=(\sqrt2-1)^2=(\sqrt2)^2-2\sqrt2+1^2=2-2\sqrt2+1=3-2\sqrt2\\ \\ m_a=\dfrac{a+b}{2}=\dfrac{3-2\sqrt2+3+2\sqrt2}{2}=\dfrac{6}{2}=3\\ \\ \\ m_g=\sqrt{a\cdot b}=\sqrt{(3-2\sqrt2)(3+2\sqrt2)}=\sqrt{3^2-(2\sqrt2)^2}=\sqrt{9-8}=1\\ \\ \\ \dfrac{^{b)}1}{\ a}+\dfrac{^{a)}1}{\ b}=\dfrac{b+a}{a\cdot b}=\dfrac{6}{1}=6\in\mathbb{N}$