\(\left(\sqrt{2x+3}+\sqrt{2x-3}\right)^2=\sqrt{2x-3}^2+2\sqrt{\left(2x+3\right)\left(2x-3\right)}+\sqrt{2x-3}^2=2x-3+2x+3+2\sqrt{4x^2-9}=4x+2\sqrt{4x^2-9}\)
\(\left(\sqrt{2x+y}+\sqrt{2x-y}\right)^2=2x+y+2x-y+2\sqrt{\left(2x+y\right)\left(2x-y\right)}=4x+2\sqrt{4x^2-y^2}\)
c) \(\left(\sqrt{2x+3}+\sqrt{2x-3}\right)^2\)
d)\(\left(\sqrt{2x+y}+\sqrt{2x-y}\right)^2\)
e) \(\left(\sqrt{5x-2}-\sqrt{5x+2}\right)^2\)
f) \(\left(\sqrt{6x+1}-\sqrt{6x-1}\right)^2\)
Tính giá trị của biểu thức
c) \(\left(\sqrt{2x+3}+\sqrt{2x-3}\right)^2\)
d) \(\left(\sqrt{2x+y}+\sqrt{2x-y}\right)^2\)
e) \(\left(\sqrt{6x+1}-\sqrt{6x-1}\right)^2\)
f) \(\left(\sqrt{5x-2}-\sqrt{5x+2}\right)^2\)
g) \(\left(\sqrt{5x-2}+\sqrt{5x+2}\right)^2\)
h) (\(\left(\sqrt{x+y}-\sqrt{x-y}\right)^2\)
Rút gọn:
\(A=1-\left[\dfrac{2x\sqrt{x}+x-\sqrt{x}}{1+x\sqrt{x}}+\dfrac{2x-1+\sqrt{x}}{1-x}\right]\cdot\left[\dfrac{\left(x-\sqrt{x}\right)\left(1-\sqrt{x}\right)}{2\sqrt{x}-1}\right]\)
\(B=\left[1:\frac{2x-1}{x-x^2}\right]\cdot\left[\frac{2x^3+x^2-x}{x^3-1}-2-\frac{1}{x-1}\right]\)
Tìm x để B=3A,biếtA=\(\left(\frac{5+2\sqrt{6}}{\sqrt{3}+\sqrt{2}}+\frac{5-2\sqrt{6}}{\sqrt{3}-\sqrt{2}}\right)\) /\(\left(\frac{1}{2\sqrt{5}+3\sqrt{2}}-\frac{1}{2\sqrt{5}-3\sqrt{2}}\right)\)
B=\(\frac{2x^4-x^3+2x^2+x-4}{2x^3-x^2-2x+1}\)
giair hpt: \(\hept{\begin{cases}\sqrt{7x+y}+\sqrt{2x+y}=5\\\sqrt{2x+y}+x-y=2\end{cases}}\)
\(\hept{\begin{cases}\sqrt{y}.\left(\sqrt{x}+\sqrt{x+3}\right)=3\\\sqrt{x}+\sqrt{y}=x+1\end{cases}}\)
Giải phương trình sau "
a, \(\sqrt{2x-1}=\sqrt{x^2+2x-5}.\)
b, \(\sqrt{x\left(x^3-3x+1\right)}=\sqrt{x\left(x^3-x\right)}\)
c, \(\sqrt{4x+1}-\sqrt{3x+4}=\sqrt{x-2}\)
d, \(\sqrt{x-1}-\sqrt{5x-1}=\sqrt{3x-2}\)
e, \(\sqrt{x+2}-\sqrt{2x-3}=\sqrt{3x-5}\)
f, \(\sqrt{x\left(x-1\right)+\sqrt{x\left(2x-1\right)}=x}\)
g, \(\sqrt{x+1}+\sqrt{x-1}=2\)
h, \(\sqrt{2x-3}-\sqrt{4x+3}=-3\)
Mn giúp với cần gấp bài toan nâng co giải dc thì tick nhiều
Giải phương trình:
a)\(\sqrt{1+x}+\sqrt{8-x}+\sqrt{\left(1+x\right)\left(8-x\right)}=3\)
b)\(\left(4x-1\right)\sqrt{x^2+1}=2x^2+2x+1\)
c)\(x^2+\sqrt{x+5}=5\)
Giair phương trình sau :
\(5+x=2\sqrt{\left(4-x\right)\left(2x-2\right)}=4\left(\sqrt{4-x}+\sqrt{2x-2}\right)\)
Giải phương trình vô tỉ :
a) \(\left(\sqrt{x+3}-\sqrt{x-1}\right)\left(x^2+\sqrt{x^2+4x+3}\right)=2x\)
b) \(\sqrt{2x+4}-2\sqrt{2-x}=\frac{6x-4}{\sqrt{x^2+4}}\)
c) \(\sqrt{3x^2-4x+2}+\sqrt{3x+1}+\sqrt{2x-1}+6x^3-7x^2-3=0\)
d) \(\sqrt{x^2+15}=3x-2+\sqrt{x^2+8}\)
