Bài 2: Căn thức bậc hai và hằng đẳng thức căn bậc hai của bình phương
Các câu hỏi tương tự
tính:
a,\(\sqrt{9-4\sqrt{5}}-\sqrt{5}\)
b,\(\sqrt{7-4\sqrt{3}}+\sqrt{4-2\sqrt{3}}\)
c,\(\dfrac{x-49}{\sqrt{x}-7}\)
d,\(\sqrt{4+2\sqrt{3}}-\sqrt{13+4\sqrt{3}}\)
e,\(2+\sqrt{17-4\sqrt{9+4\sqrt{45}}}\)
giải phương trình
1/\(\sqrt{x^2}-4x+8\) +\(\sqrt{x^2-4x+13}=17-2x^2+8x\)
2/\(\sqrt{3x^2+6x+7}+\sqrt{5x^2+10x-24}=4-2x-x^2\)
1. So sánh x và y :
x = \(\dfrac{30-2\sqrt{45}}{4}\) và y = \(\sqrt{17}\)
2. Tìm x,y,z bt :
a, x+y+z+8 = \(2\sqrt{x-1}\)+ \(4\sqrt{y-2}\)+ \(6\sqrt{z-3}\)
Tính
a)\(\sqrt{4+2\sqrt{3}}-\sqrt{4-2\sqrt{3}}\)
b)\(\sqrt{9-4\sqrt{5}}-\sqrt{9+4\sqrt{5}}\)
c) \(\sqrt{17-12\sqrt{2}}-\sqrt{24-8\sqrt{8}}\)
d)\(\sqrt{17-3\sqrt{32}}+\sqrt{17+3\sqrt{32}}\)
Giải các phương trình sau:a) sqrt{x^2-4+4}2-xb) sqrt{4x-8}-dfrac{1}{5}sqrt{25x-50}3sqrt{x-2}-1c) sqrt{x-1}+sqrt{9x-9}-sqrt{4x-4}4d) dfrac{1}{2}sqrt{x-2}-4sqrt{dfrac{4x-8}{9}}+sqrt{9x-18}-50e)sqrt{49-28x+4x^2}-50f) sqrt{4x-20}+sqrt{x-5}-dfrac{1}{3}sqrt{9x-45}4g) x2 - 4x - 2sqrt{2x-5}+50h)sqrt{3x-2}sqrt{x+1}i) x + y + z + 8 2sqrt{x-1}+4sqrt{y-2}+6sqrt{z-3}k) sqrt{x^2-3x}-sqrt{x-3}0l)sqrt{x^2-4}+sqrt{x-2}0m) 4sqrt{x+1}x^2-5x+14n) sqrt{x^2-6x+9}-sqrt{4x^2+4x+1}0
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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) \(\sqrt{x^2-6x+9}-\sqrt{4x^2+4x+1}=0\)
\(B=\frac{3\sqrt{x}+4}{3\sqrt{x}-2}-\frac{42\sqrt{x}+34}{15x+11\sqrt{x}-14}\)
Rút gọn :
dfrac{sqrt{x+sqrt{4left(x-1right)}}-sqrt{x-sqrt{4left(x-1right)}}}{sqrt{x^2-4left(x-1right)}}.left(sqrt{x-1}-dfrac{1}{sqrt{x-1}}right)
b)left(sqrt{2}+1right)left(sqrt{3}+1right)left(sqrt{6}+1right)left(5-2sqrt{2}-sqrt{3}right)
c)left(sqrt{5}+1right)left(sqrt{7}+1right)left(sqrt{35}+1right)left(34-4sqrt{7}-6sqrt{5}right)
d) left(sqrt{7}+1right)left(2sqrt{2}-1right)left(2sqrt{14}-1right)left(55+12sqrt{2}-7sqrt{7}right)
e)left(3sqrt{2}+1right)left(2sqrt{3}+1right)left(6sqrt{6}+1...
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Rút gọn :
\(\dfrac{\sqrt{x+\sqrt{4\left(x-1\right)}}-\sqrt{x-\sqrt{4\left(x-1\right)}}}{\sqrt{x^2-4\left(x-1\right)}}.\left(\sqrt{x-1}-\dfrac{1}{\sqrt{x-1}}\right)\)
b)\(\left(\sqrt{2}+1\right)\left(\sqrt{3}+1\right)\left(\sqrt{6}+1\right)\left(5-2\sqrt{2}-\sqrt{3}\right)\)
c)\(\left(\sqrt{5}+1\right)\left(\sqrt{7}+1\right)\left(\sqrt{35}+1\right)\left(34-4\sqrt{7}-6\sqrt{5}\right)\)
d) \(\left(\sqrt{7}+1\right)\left(2\sqrt{2}-1\right)\left(2\sqrt{14}-1\right)\left(55+12\sqrt{2}-7\sqrt{7}\right)\)
e)\(\left(3\sqrt{2}+1\right)\left(2\sqrt{3}+1\right)\left(6\sqrt{6}+1\right)\left(215-34\sqrt{3}-33\sqrt{2}\right)\)
a. \(\sqrt{x+3-4\sqrt{x-1}}+\sqrt{x+8+6\sqrt{x-2}}=5\)
b. \(\sqrt{x+2\sqrt{x-1}}+\sqrt{x-2\sqrt{x-1}}=x-1\)
c. \(\sqrt{3x+8+6\sqrt{3x-1}}+\sqrt{3x+8-6\sqrt{3x-1}}=3x+4\)
d. \(\sqrt{x+2+3\sqrt{2x-5}}+\sqrt{x-2-2\sqrt{2x-5}}=2\sqrt{2}\)
Bài 2: Tìm sự xác định của các biểu thức chứa căn
1 sqrt{6x+1}
2 sqrt{dfrac{-3}{2+x}}
3 sqrt{-8x}
4 sqrt{4-5x}
5 sqrt{left(x+5right)^2}
6 sqrt{dfrac{sqrt{6}-4}{m+2}}
7 sqrt{left(sqrt{3}-xright)^2}
8 dfrac{16x-1}{sqrt{x}-7}
9 sqrt{x^2+2x+1}
10 sqrt{2x+5}
11 sqrt{-12x+5}
12 dfrac{3}{sqrt{12x-1}}
13 2 - 4sqrt{5x+8}
14 sqrt{x^2+3}
15 sqrt{dfrac{5}{x^2}}
16 sqrt{dfrac{x+3}{7-x}}
17 sqrt{x-x^2}
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Bài 2: Tìm sự xác định của các biểu thức chứa căn
1> \(\sqrt{6x+1}\)
2> \(\sqrt{\dfrac{-3}{2+x}}\)
3> \(\sqrt{-8x}\)
4> \(\sqrt{4-5x}\)
5> \(\sqrt{\left(x+5\right)^2}\)
6> \(\sqrt{\dfrac{\sqrt{6}-4}{m+2}}\)
7> \(\sqrt{\left(\sqrt{3}-x\right)^2}\)
8> \(\dfrac{16x-1}{\sqrt{x}-7}\)
9> \(\sqrt{x^2+2x+1}\)
10> \(\sqrt{2x+5}\)
11> \(\sqrt{-12x+5}\)
12> \(\dfrac{3}{\sqrt{12x-1}}\)
13> 2 - \(4\sqrt{5x+8}\)
14> \(\sqrt{x^2+3}\)
15> \(\sqrt{\dfrac{5}{x^2}}\)
16> \(\sqrt{\dfrac{x+3}{7-x}}\)
17> \(\sqrt{x-x^2}\)