d: \(a-\sqrt{ab}=\sqrt{a}\left(\sqrt{a}-\sqrt{b}\right)\)
e: \(=\left(\sqrt{x}+1\right)^2\)
i: \(=\left(\sqrt{x}-3\right)\left(x+3\sqrt{x}+9\right)\)
k: \(=\left(\sqrt{x}+1\right)\left(x-\sqrt{x}+1\right)\)
Phân tích thành nhân tử:
a. x+ \(2\sqrt{x}\)
b. x- \(\sqrt{x}\)
c. \(x\sqrt{x}+x-\sqrt{x}-1\)
d. a - \(\sqrt{ab}\)
e. x+ \(2\sqrt{x}+1\)
f. \(x-4\sqrt{x}+4\)
g. x-4
h. \(a\sqrt{a}+b\sqrt{b}\)
i. \(x\sqrt{x}-27\)
k. \(x\sqrt{x}+1\)
j. x2- \(\sqrt{x}\)
Bài 1: Tính
a) \(\sqrt{9-\sqrt{17}}\cdot\sqrt{9+\sqrt{17}}\)
b) \(\sqrt{4-\sqrt{7}}-\sqrt{4+\sqrt{7}}\)
c) \(\left(\sqrt{3-\sqrt{5}}+\sqrt{3+\sqrt{5}}\right)^2\)
d) \(\sqrt{2+\sqrt{3}}\cdot\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{3}}}}\cdot\sqrt{2-\sqrt{2+\sqrt{2+\sqrt{3}}}}\)
e) \(\sqrt{\frac{8+\sqrt{15}}{2}}+\sqrt{\frac{8-\sqrt{15}}{2}}\)
Bài 2: Giải pt:
a) \(\sqrt{x+3-4\sqrt{x-1}}+\sqrt{x+8-6\sqrt{x-1}}=1\)
b) \(\sqrt{x+\sqrt{x-11}}+\sqrt{x-\sqrt{x-11}}=4\)
c) \(\sqrt{x+2+3\sqrt{2x-5}}+\sqrt{x-2-\sqrt{2x-5}}=2\sqrt{2}\)
d) \(\sqrt{x-4}+\sqrt{6-x}=x^2-10x+27\)
e) \(\sqrt{2x+1}+\sqrt{17-2x}=x^4-8x^3+17x^2-8x+22\)
f) \(\sqrt{x+x^2}+\sqrt{x-x^2}=x+1\)
g) \(\sqrt{3x^2+12x+16}+\sqrt{y^2-4y+13}=5\)
Bài 3: Cho biểu thức:
P= \(\frac{\sqrt{x+4\sqrt{x-4}}+\sqrt{x-4\sqrt{x-4}}}{\sqrt{\frac{16}{x^2}-\frac{8}{x}+1}}\)
a) Rút gon P
b) Tìm x để P đạt GTNN, tìm GTNN đó.
c) Tìm x \(\in\) Z để P \(\in\) Z
@Nguyễn Văn Đạt@Akai Haruma Help me please~~~~ Giải thích cẩn thân hộ với.
Tìm X để căn thức sau có nghĩa
a) \(\sqrt{1-2x}\) c) \(\sqrt{\frac{4}{5x-3}}\) e)\(\sqrt{1-x^3}\)
b) \(\sqrt{\frac{2}{1-x^2}}\) d) \(\sqrt{\frac{1}{\sqrt[3]{9-x^2}}}\) g) \(\sqrt{4x^2-9}\)
h) \(\sqrt{\frac{5-2x}{x^2+4}}\) i) \(\sqrt[3]{\frac{1-x}{1+x}}\) j) \(\frac{1}{x+\sqrt{x-4}}\)
k) \(\sqrt{\frac{3+x^2}{4-x^2}}\) l) \(\sqrt{\frac{x^2}{1+x}}\)
a) \(\sqrt{x-3}-\sqrt{10-x}\)
b) \(\sqrt{x+4}+\dfrac{2-X}{x^2-16}\)
c) \(\dfrac{\sqrt{2x-3}}{\sqrt{x-4}}\)
d) \(\dfrac{\sqrt{2x-1}}{3x+2}\)
e) \(\dfrac{-2}{\sqrt{x^2+2x+2}}\)
Cho biểu thức
1) A=\(\dfrac{\sqrt{x}+2}{2\sqrt{x}-4}+\dfrac{\sqrt{x}-2}{2\sqrt{x}+4}\)
a. Rút gọn A
b. Tìm x để A=8
2) C= \(\left(\dfrac{1}{\sqrt{x}-1}+\dfrac{1}{x-\sqrt{x}}\right):\dfrac{\sqrt{x}+1}{\left(\sqrt{x}-1\right)^2}\)
a. Rút gọn C
b.Tìm x để C= -8
3) D=\(\left(\dfrac{\sqrt{x}}{\sqrt{x}+2}+\dfrac{\sqrt{x}}{\sqrt{x}-2}\right)\dfrac{\sqrt{4x}}{x-4}\)
a.Rút gọn D
b.Tìm x để D>3
Giải phương trình :
a, \(\sqrt{x+1}=x-1\)
b, \(x-\sqrt{2x+3}=0\)
c, \(\sqrt{x-2}-3\sqrt{\left(x-2\right)\left(x+2\right)}=0\)
d, \(\sqrt{\sqrt{3}-x}=x\sqrt{\sqrt{3}+x}\)
e, \(2\sqrt{x+3}=9x^2-x-4\)
f, \(\sqrt{x+1}-\sqrt{x-7}=\sqrt{12-x}\)
g, \(\sqrt{2x+5}-\sqrt{3x-5}=2\)
h, \(\sqrt{x}-\sqrt{x-1}-\sqrt{x-4}+\sqrt{x+9}=0\)
i, \(x^2+2x-\sqrt{x^2+2x+1}-5=0\)
k, \(\sqrt{x+8-6\sqrt{x+1}}=4\)
l, \(\sqrt{x^2-8x+16}+\sqrt{x^2-10x+25}=9\)
Làm được phần nào thì giúp mình nha đang cần gấp !!!
Dùng biểu thức liên hợp:
a)\(\sqrt{2x-1}-\sqrt{x+1}=2x-4\). f)\(3\sqrt{x+1}+3\sqrt{x-1}=4x+1\).
b)\(\sqrt{2x^2-3x+10}+\sqrt{2x^2-5x+4}=x+3\).
c)\(\sqrt{x+2}-\sqrt{3-x}=x^2-6x+9\).
d)\(\sqrt{x}-\sqrt{x-1}=\sqrt{x+8}-\sqrt{x+3}.\)
e)\(\sqrt{x^2+x}-\sqrt{x^2-3}=\sqrt{2x^2-x-2}-\sqrt{2x^2+1}\)
1, \(\dfrac{a+4\sqrt{a}+4}{\sqrt{a}+2}+\dfrac{4-a}{\sqrt{a}-2}\)
2, \(\dfrac{\left(\sqrt{x}+\sqrt{y}\right)-4\sqrt{xy}}{\sqrt{x}-\sqrt{y}}+\dfrac{y\sqrt{x}-x\sqrt{y}}{\sqrt{xy}}\)
3, \(\dfrac{9\sqrt{a}-b\sqrt{5}}{\sqrt{a}-\sqrt{5}}+\sqrt{ab}\)
4, \(\left(\dfrac{1-a\sqrt{a}}{1-\sqrt{a}}+\sqrt{a}\right)\left(\dfrac{1-\sqrt{a}}{1-a}\right)\)
5, \(\dfrac{\sqrt{x}+1}{x-1}-\dfrac{x+2}{x\sqrt{x}-1}-\dfrac{\sqrt{x}+1}{x+\sqrt{x}+1}\)
1. Phân tích ra thừa số
a.\(\sqrt{ab}-\sqrt{ac}+\sqrt{bc}+b\)
b.x-y-3(\(\sqrt{x}-\sqrt{y}\))
c. \(\sqrt{x^2-y^2}\)-x+y
2. GPT
a.\(\sqrt{\sqrt{5}-\sqrt{3}x}\)=\(\sqrt{8+2\sqrt{15}}\)
b.\(\sqrt{2+\sqrt{3+\sqrt{x}}}=3\)
Giải phương trình
a,\(\sqrt{x^2+x-20}=\sqrt{x-4}\)
b,\(\sqrt{x+1}+\sqrt{2-x}=\sqrt{6}\)
c,\(\sqrt{x+2\sqrt{x-1}=2}\)
d,\(\sqrt{2x-2+2\sqrt{2x-3}+}\sqrt{2x+13+8\sqrt{2x-3}=}5\)
e, \(\sqrt{x^2-1}-x^2+1=0\)
f,\(\sqrt{x^2-9}+\sqrt{x^2-6x+9}=0\)
g,\(\sqrt{x^2-2x+1}+\sqrt{x^2-4x+4}=3\)
