\(\Leftrightarrow\left\{{}\begin{matrix}x+\dfrac{1}{3}y=\dfrac{7}{3}\\x-\dfrac{1}{2}y=-\dfrac{1}{6}\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}\dfrac{5}{6}y=\dfrac{5}{2}\\x+\dfrac{1}{3}y=\dfrac{7}{3}\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=3\\x=\dfrac{4}{3}\end{matrix}\right.\)

Lời giải:

Lấy PT(1) trừ PT(2) theo vế:

$\frac{y}{3}+\frac{y}{2}=\frac{7}{3}+\frac{1}{6}$

$\Leftrightarrow \frac{5}{6}y=\frac{5}{2}$
$\Leftrightarrow y=3$

$x=\frac{7}{3}-\frac{y}{3}=\frac{7}{3}-1=\frac{4}{3}$

Giúp em giải với huhu 

a) A = \(\sum\limits^{50}_1\left(2x\right)-\sum\limits^{50}_1\left(2x-1\right)\) = 5050

b) B = \(\sum\limits^{2010}_1x^3\) = 4084663313000

câu 21

làm một con có vẻ rắc rối nhất ví dụ thôi

\(\dfrac{\sqrt{5+2\sqrt{6}}+\sqrt{8-2\sqrt{15}}}{\sqrt{7+2\sqrt{10}}}=\dfrac{\sqrt{\left(\sqrt{2}+\sqrt{3}\right)^2}+\sqrt{\left(\sqrt{5}-\sqrt{3}\right)^2}}{\sqrt{\left(\sqrt{5}+\sqrt{2}\right)^2}}=\dfrac{\sqrt{2}+\sqrt{5}}{\sqrt{5}+\sqrt{2}}=1\)\(=\dfrac{\sqrt{2}+\sqrt{5}}{\sqrt{5}+\sqrt{2}}=1\)

a: Thay x=2 vào (P),ta được:

y=2^2/2=2

2: Thay x=2 và y=2 vào (d), ta được:

m-1+2=2

=>m-1=0

=>m=1

b: \(\sqrt{8-2\sqrt{15}}-\sqrt{5}\)

\(=\sqrt{5}-\sqrt{3}-\sqrt{5}\)

\(=-\sqrt{3}\)

c: \(\sqrt{11-6\sqrt{2}}=3-\sqrt{2}\)

d: \(\sqrt{5-2\sqrt{6}}=\sqrt{3}-\sqrt{2}\)

a) \(\dfrac{1}{\sqrt[]{x}-1}+\dfrac{1}{1+\sqrt[]{x}}+1\left(x\ge0;x\ne1\right)\)

\(=\dfrac{\sqrt[]{x}+1+\sqrt[]{x}-1+x-1}{\left(\sqrt[]{x}-1\right)\left(\sqrt[]{x}+1\right)}\)

\(=\dfrac{x+2\sqrt[]{x}-1}{x-1}\)

\(=\dfrac{x-1+2\sqrt[]{x}}{x-1}\)

\(=1+\dfrac{2\sqrt[]{x}}{x-1}\)

b) \(\dfrac{1}{\sqrt[]{x}+2}-\dfrac{2}{\sqrt[]{x}-2}-\dfrac{4}{4-x}\left(x\ge0;x\ne4\right)\)

\(=\dfrac{\sqrt[]{x}-2-2\left(\sqrt[]{x}+2\right)+4}{\left(\sqrt[]{x}+2\right)\left(\sqrt[]{x}-2\right)}\)

\(=\dfrac{\sqrt[]{x}-2-2\sqrt[]{x}-4+4}{\left(\sqrt[]{x}+2\right)\left(\sqrt[]{x}-2\right)}\)

\(=\dfrac{-\sqrt[]{x}-2}{\left(\sqrt[]{x}+2\right)\left(\sqrt[]{x}-2\right)}\)

\(=\dfrac{-\left(\sqrt[]{x}+2\right)}{\left(\sqrt[]{x}+2\right)\left(\sqrt[]{x}-2\right)}\)

\(=\dfrac{-1}{\sqrt[]{x}-2}\)

\(\Delta'=4-\left(m+1\right)\ge0\Rightarrow m\le3\)

Theo hệ thức Viet: \(\left\{{}\begin{matrix}x_1+x_2=4\\x_1x_2=m+1\end{matrix}\right.\)

\(x_1^2+x_2^2=5\left(x_1+x_2\right)\)

\(\Leftrightarrow\left(x_1+x_2\right)^2-2x_1x_2=5\left(x_1+x_2\right)\)

\(\Leftrightarrow16-2\left(m+1\right)=20\)

\(\Leftrightarrow m=-3\) (thỏa mãn)

a. Ta có: \(x^2-4x+m+1=0\)

Thay m=2 ta được: \(x^2-4x+2+1=0\Leftrightarrow x^2-4x+3=0\Leftrightarrow\left[{}\begin{matrix}x=3\\x=1\end{matrix}\right.\)

b. Để phương trình có 2 nghiệm phân biệt thì \(\Delta=\left(-4\right)^2-4.1.\left(m+1\right)>0\)

\(\Leftrightarrow16-4\left(m+1\right)>0\Leftrightarrow16>4\left(m+1\right)\Leftrightarrow4>m+1\Leftrightarrow m< 3\)

Áp dụng định lí Vi-et ta có: \(\left\{{}\begin{matrix}x_1+x_2=4\\x_1x_2=m+1\end{matrix}\right.\)

Theo đề ta có: \(x_1^2+x_2^2=5\left(x_1+x_2\right)\)

\(\Leftrightarrow\left(x_1+x_2\right)^2-2x_1x_2=5\left(x_1+x_2\right)\)

\(\Leftrightarrow\left(4\right)^2-2\left(m+1\right)=5.4\)

\(\Leftrightarrow16-2m-2=20\Leftrightarrow m=-3\) (TM)