\(x+4\sqrt{x}+4=\left(\sqrt{x}\right)^2+2.2.\sqrt{x}+2^2=\left(\sqrt{x}+2\right)^2\)
\(x+4\sqrt{x}+4=\left(\sqrt{x}+2\right)^2\)
Rút gọn:
C= (\(\dfrac{\sqrt{x+1}}{x-4}\) - \(\dfrac{\sqrt{x-1}}{x+4\sqrt{x}+4}\) ) . \(\dfrac{x\sqrt{x}+2x-4\sqrt{x}-8}{\sqrt{x}}\)
(x> 0; x ≠ 4)
Rút gọn
a) \(\dfrac{x^5-2x^4+2x^3-4x^2-3x+6}{x+4}\)
b) \(\dfrac{x^4-4x^2+3}{x^4+6x^2-7}\)
c) \(\dfrac{x^4+x^3-x-1}{x^4+x^3+2x^2+x+1}\)
4 x 4 + 4 x 4 + 4 - 4 x 4 =............
giả pt
\(\sqrt{x+4\sqrt{x}+4}+\sqrt{x-4\sqrt{x}+4}=4\)
\(2x^4+8x=4\sqrt{4+x^4}+4\sqrt{x^4-4}\)
\(^{x^3-3x^2-8x+40-8\sqrt[4]{4x+4}=0}\)
\(\sqrt[4]{x}+\sqrt[4]{1-x}+\sqrt{x}-\sqrt{1-x}=\sqrt{2}+\sqrt[4]{8}\)
Cho Q= \(\dfrac{\sqrt{x}-1}{\sqrt{x}+4}\) + \(\dfrac{9\sqrt{x}-4}{x-16}\) - \(\dfrac{4\sqrt{x}-4x}{\sqrt{x}-4}\)
Chứng minh Q= \(\dfrac{x-3\sqrt{x}}{\sqrt{x}-4}\)
Giải các phương trình sau:
a \(x^4-x^2-56=0\)
b \(\left(x-2\right)^4+\left(x+2\right)^4=32\)
c \(\left(x+3\right)^4+\left(x+5\right)^4=16\)
d \(\left(6-x\right)^4+\left(8-x\right)^4=80\)
CMR: \(\frac{\sqrt{x^4+y^4}+\sqrt{x^4-y^4}}{\sqrt{x^4+y^4}-\sqrt{x^4-y^4}}-\sqrt{\frac{x^8}{y^8}-1}=\frac{x^4}{y^4}\)
1, \(\sqrt{x-1}+\sqrt{x-4}=5\)
2, \(2x-7\sqrt{x}+5=0\)
3, \(\sqrt{2x+1}+\sqrt{x-3}=2\sqrt{x}\)
4, \(x-4\sqrt{x}+2021\sqrt{x-4}+4=0\)
5, \(\sqrt{2x-3}-\sqrt{x+1}=7\left(4-x\right)\)
A=\(\left(\dfrac{\sqrt{x}+1}{x-4}-\dfrac{\sqrt{x}-1}{x-4\sqrt{x}+4}\right)\)\(\dfrac{x\sqrt{x}-2x-4\sqrt{x}-8}{\sqrt{x}}\)
