Răspuns:
Explicație pas cu pas:
ex2
[tex]a=\frac{2}{\sqrt{2}}+1,~b=\sqrt{(1-\sqrt{2})^{2}}\\a=\frac{2\sqrt{2}}{(\sqrt{2})^{2}}+1=\frac{2\sqrt{2} }{2}+1=\sqrt{2}+1.\\b=\sqrt{(1-\sqrt{2})^{2}}=|1-\sqrt{2}|=|\sqrt{2}-1|=\sqrt{2}-1.\\ma=\frac{a+b}{2}=\frac{\sqrt{2}+1+\sqrt{2}-1}{2}=\frac{2\sqrt{2} }{2}=\sqrt{2} \\mg=\sqrt{a*b}=\sqrt{(\sqrt{2}+1)(\sqrt{2}-1)}=\sqrt{(\sqrt{2})^{2}-1^{2} }=\sqrt{2-1}=\sqrt{1}=1\\[/tex]
ex3. A(-2;5), B(4;-4)
[tex]AB=\sqrt{(x_{A}-x_{B})^{2}+(y_{A}-y_{B})^{2}}=\sqrt{(-2-4)^{2}+(5-(-4))^{2}}=\sqrt{36+81}=\sqrt{117}\\[/tex]
ex4. E(x)=4x²+4x+11=(2x)²+2·2x·1+1²+10=(2x+1)²+10
Deci E(x)≥10. ⇒min(E(x))=10 pentru 2x+1=0, sau 2x=-1, sau x=-1/2
ex5. Inmultind fiecare termen a ecua'iei cu 24, obtinem:
3(x-5)-6(3x-2)-3·3=4(2x+3)-2(x-6), ⇒3x-15-18x+12-9=8x+12-2x+12⇒
⇒3x-18x-8x+2x=12+12+9-12+15, ⇒-21x=36, ⇒x=-36/21=-12/7
