Bạn giải hệ \(\hept{\begin{cases}7x+7y=112000\\3x+2y=41000\end{cases}}\)với x là giá 1 cân cam ; y là giá 1 cân lê

good luck:))

tớ làm bất thôi, hình nhường bạn khác :P

Ta có \(\frac{a+1}{b^2+1}=a+1-\frac{b^2\left(a+1\right)}{b^2+1}\ge a+1-\frac{b^2\left(a+1\right)}{2b}=a+1-\frac{ab+b}{2}\left(1\right)\)(bđt AM-GM)

Tương tự \(\frac{b+1}{c^2+1}\ge b+1-\frac{bc+c}{2}\left(2\right)\)

       \(\frac{c+1}{a^2+1}\ge c+1-\frac{ca+a}{2}\left(3\right)\)

Cộng từng vế bđt (1),(2),(3) ta được

\(VT\ge a+1+b+1+c+1-\frac{a+b+c-ab-bc-ca}{2}=6-\frac{3-ab-bc-ca}{2}\ge3\)

(do \(\left(a+b+c\right)^2\ge3\left(ab+bc+ca\right)\Rightarrow ab+bc+ca\le3\))

Dấu "=" xảy ra khi a=b=c=1

1/ \(LHS-RHS=\Sigma_{cyc}\frac{b\left(a+1\right)\left(b-1\right)^2}{2\left(b^2+1\right)}+\frac{3\left(a-b\right)^2+\left(a+b-2c\right)^2}{24}\ge0\)

Đẳng thức xảy ra khi \(a=b=c=1\)

Đáp án:B

Vì trong 1 tứ giác nội tiếp tổng 2 góc đối bằng 180 độ 

\(b=\frac{3+2\sqrt{3}}{\sqrt{3}}+\frac{2\sqrt{2}}{\sqrt{2}+1}-\left(3+\sqrt{3}-2\sqrt{2}\right)\)\(=\sqrt{3}+2+\frac{2\sqrt{2}\left(\sqrt{2}-1\right)}{\left(\sqrt{2}+1\right)\left(\sqrt{2}-1\right)}-\left(3+\sqrt{3}-2\sqrt{2}\right)\)

\(=\sqrt{3}+2+2\sqrt{2}\left(\sqrt{2}-1\right)-\left(3+\sqrt{3}-2\sqrt{2}\right)\)

\(=\sqrt{3}+2+4-2\sqrt{2}-3-\sqrt{3}+2\sqrt{2}\)

\(=3\)

\(\sqrt{2020}+\sqrt{-\frac{3}{x+3}}\)

Căn thức trên có nghĩa khi:\(\hept{\begin{cases}x+3\ne0\\-\frac{3}{x+3}>0\end{cases}\Leftrightarrow\hept{\begin{cases}x\ne-3\\x+3< 0\end{cases}\Leftrightarrow\hept{\begin{cases}x\ne-3\\x< -3\end{cases}}}}\)

\(\Rightarrow x< -3\)

Ta có : \(D=\left(\sqrt{57}+3\sqrt{6}+\sqrt{38}+6\right)\left(\sqrt{57}-3\sqrt{6}-\sqrt{38}+6\right)\)

\(=\left(\sqrt{57}+6\right)^2-\left(3\sqrt{6}+\sqrt{38}\right)^2\)

\(=57+12\sqrt{57}+36-\left(54+12\sqrt{57}+38\right)\)

\(=93-92=1\)

Vậy : \(D=1\)

\(D=\left(\sqrt{57}+3\sqrt{6}+\sqrt{38}+6\right)\left(\sqrt{57}-2\sqrt{6}-\sqrt{38}+6\right)\)

\(=\left(\sqrt{57}+6\right)^2-\left(3\sqrt{6}+\sqrt{38}\right)^2\)

\(=\left(93+12\sqrt{57}\right)-\left(92+12\sqrt{57}\right)\)

\(=1\)