a) \(\sqrt{9x^2}\) = 12 ⇔ / 3x/ = 12
⇔ \(\left[{}\begin{matrix}3x=12\\3x=-12\end{matrix}\right.\)
⇔\(\left[{}\begin{matrix}x=4\\x=-4\end{matrix}\right.\)
b) \(\sqrt{4x^2}\) = / -18 / ⇔ \(\sqrt{4x^2}\) = 18
⇔ / 2x / = 18
⇔ \(\left[{}\begin{matrix}2x=18\\2x=-18\end{matrix}\right.\)
⇔ \(\left[{}\begin{matrix}x=9\\x=-9\end{matrix}\right.\)
Giải các phương trình sau:
a) \(\sqrt{x^2-4+4}=2-x\)
b) \(\sqrt{4x-8}-\dfrac{1}{5}\sqrt{25x-50}=3\sqrt{x-2}-1\)
c) \(\sqrt{x-1}+\sqrt{9x-9}-\sqrt{4x-4}=4\)
d) \(\dfrac{1}{2}\sqrt{x-2}-4\sqrt{\dfrac{4x-8}{9}}+\sqrt{9x-18}-5=0\)
e)\(\sqrt{49-28x+4x^2}-5=0\)
f) \(\sqrt{4x-20}+\sqrt{x-5}-\dfrac{1}{3}\sqrt{9x-45}=4\)
g) x2 - 4x - 2\(\sqrt{2x-5}+5=0\)
h)\(\sqrt{3x-2}=\sqrt{x+1}\)
i) x + y + z + 8 = \(2\sqrt{x-1}+4\sqrt{y-2}+6\sqrt{z-3}\)
k) \(\sqrt{x^2-3x}-\sqrt{x-3}=0\)
l)\(\sqrt{x^2-4}+\sqrt{x-2}=0\)
m) \(4\sqrt{x+1}=x^2-5x+14\)
n) \(\sqrt{x^2-6x+9}-\sqrt{4x^2+4x+1}=0\)
Tìm x, biết:
a. \(\sqrt{x^2}=7;\)
b. \(\sqrt{x^2}=\left|-8\right|;\)
c. \(\sqrt{4x^2}=6;\)
d. \(\sqrt{9x^2}=\left|-12\right|.\)
Tìm \(x\), biết :
a) \(\sqrt{9x^2}=2x+1\)
b) \(\sqrt{x^2+6x+9}=3x-1\)
c) \(\sqrt{1-4x+4x^2}=5\)
d) \(\sqrt{x^4}=7\)
Bài 3: Giari phương trình \(\sqrt{A}\)=B
a> \(\sqrt{3x-1}\)
b> \(\sqrt{-3x+4}\) = 12
c> \(\sqrt{x^2-8x+16}\) = 4
d> \(\sqrt{9\left(x-1\right)}\) = 21
g> \(\sqrt{2-3x}\) = 10
h> \(\sqrt{4x}\) = \(\sqrt{5}\)
i> \(\sqrt{4-5x}\) = 12
p> \(\sqrt{16x}\) = 8
q> \(\sqrt{\left(x-3\right)^2}\) = 3
v> \(\sqrt{\dfrac{-6}{1+x}}\) = 5
w> \(\sqrt{4x-20}-3\)\(\sqrt{\dfrac{x-5}{9}}\) = \(\sqrt{1-x}\)
x> \(\sqrt{4x+8}\) + 2\(\sqrt{x+2}\) - \(\sqrt{9x+18}\) = 1
a'> \(\sqrt{x^2-6x+9}\)+x=11
z> \(\sqrt{16\left(x+1\right)^2}\) - \(\sqrt{9\left(x+1\right)}\) = 4
b'> \(\sqrt{9x+9}\) + \(\sqrt{4x+4}\) = \(\sqrt{x+1}\)
Giup minh nhe!!
1. Rut gon bieu thuc:
a) \(A=\sqrt{11-6\sqrt{2}}+3+\sqrt{2}\)
b) \(B=\sqrt{12+2\sqrt{11}}+\sqrt{12-2\sqrt{11}}\)
2. Rut gon bieu thuc:
a) \(A=\sqrt{x-2+2\sqrt{x-3}}+\sqrt{x+6+6\sqrt{x-3}},voix>=3\)
3. Tim GTNN cua bieu thuc:
a) \(A=\sqrt{4x^2-12x+9}+\sqrt{x^2-10x+25}+\sqrt{9x^2-6x+1}+\sqrt{16x^2-72x+81}\)
b) \(B=\dfrac{1}{2}\sqrt{x^2}+\sqrt{x^2-2x+1}\)
Tìm x biết:
a, \(\sqrt{4x^2}\) = 6
b, \(\sqrt{16x}\) = 8
c, \(\sqrt{9\left(x-1\right)}\) = 21
d, \(\sqrt{4\left(1-x\right)^2}-6=0\)
e, \(\sqrt{1-4x+4x^2}=5\)
f, \(\sqrt{9x^2}\) = 2x + 1
Phân tích đa thức thành nhân tử :
a. \(\sqrt{ax}+\sqrt{by}-\sqrt{ay}-\sqrt{bx}\)
b. \(\sqrt{a^2-b^2}-\sqrt{a^3+b^3}\)
c. \(x-3\sqrt{x}-18\)
d. \(x\sqrt{x}+4x-12\sqrt{x}-27\)
giải phương trình
a)\(\sqrt{x^2-6x+9}=4\)
b)\(\sqrt{4x^2-4x+1}=5x+3\)
c)\(\sqrt{x^2-9}+\sqrt{x^2-6x+9}=0\)
d)\(\sqrt{x^2+2x+1}+\sqrt{x^2-4x+4}=3\)
e)\(\sqrt{9x^2-12x+4}=\sqrt{x^2-10x+25}\)
Phân tích đa thức thành nhân tử:
a) \(\sqrt{a^2-b^2}\) - \(\sqrt{a^3+b^3}\)
b) x - \(3\sqrt{x}\) - 18
c) \(x\sqrt{x}\) + 4x - \(12\sqrt{x}\) - 27