D) ĐK x>= 1
đặt \(\sqrt{x-1}=a;\sqrt{x^3+x^2+x+1}=b\)
pt <=> \(a+b=1+ab\Rightarrow a+b-1-ab=0\)
<=> \(\left(a-1\right)\left(1-b\right)=0\)
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Rút gọn biểu thức:
1) \(\sqrt{9-4\sqrt{5}}+\sqrt{\left(25+1\right)^2}\)
2) \(\dfrac{x^2-5}{x+\sqrt{5}}\)
3) \(\dfrac{\sqrt{x^2-2x+1}}{x-1}\)
4) \(\sqrt{4+\sqrt{7}}-\sqrt{4-\sqrt{7}}\)
Rút gọndfrac{6}{sqrt{5}+1}+sqrt{dfrac{2}{3-sqrt{5}}}-dfrac{10}{sqrt{5}} B1. Với xge0,xne4.ChobiểuthứcAdfrac{x-9}{left(sqrt{x}+3right)left(sqrt{x}-2right)}-dfrac{1}{2-sqrt{x}}-dfrac{sqrt{x}}{sqrt{x}+3}Bdfrac{1}{xsqrt{x}+27}a, tính giá trị biểu thức khi B 1/4b, Rút gọn Ac, Tìm giá trị của x để A1/2d, Với C B : A. Tìm GTLN C
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Rút gọn
\(\dfrac{6}{\sqrt{5}+1}+\sqrt{\dfrac{2}{3-\sqrt{5}}}-\dfrac{10}{\sqrt{5}}\)
B1. Với \(x\ge0,x\ne4.Chobiểuthức\)
\(A=\dfrac{x-9}{\left(\sqrt{x}+3\right)\left(\sqrt{x}-2\right)}-\dfrac{1}{2-\sqrt{x}}-\dfrac{\sqrt{x}}{\sqrt{x}+3}\)
\(B=\dfrac{1}{x\sqrt{x}+27}\)
a, tính giá trị biểu thức khi B= 1/4
b, Rút gọn A
c, Tìm giá trị của x để A>1/2
d, Với C= B : A. Tìm GTLN C
1) x+1+sqrt{x^2-4x+1}3sqrt{x}2) 4x^3+x-left(x+1right)sqrt{2x+1}03) x-sqrt{x}1-sqrt{2left(x^2-x+1right)}4) sqrt{x+1}+sqrt{4-x}+sqrt{left(x+1right)left(4-xright)}55) sqrt{3x-2}+sqrt{x-1}4x-9+2sqrt{3x^2-5x+2}6) 3sqrt{x+2}-6sqrt{2-x}+4sqrt{4-x^2}10-3x
Đọc tiếp
1) \(x+1+\sqrt{x^2-4x+1}=3\sqrt{x}\)
2) \(4x^3+x-\left(x+1\right)\sqrt{2x+1}=0\)
3) \(x-\sqrt{x}=1-\sqrt{2\left(x^2-x+1\right)}\)
4) \(\sqrt{x+1}+\sqrt{4-x}+\sqrt{\left(x+1\right)\left(4-x\right)}=5\)
5) \(\sqrt{3x-2}+\sqrt{x-1}=4x-9+2\sqrt{3x^2-5x+2}\)
6) \(3\sqrt{x+2}-6\sqrt{2-x}+4\sqrt{4-x^2}=10-3x\)
Ai dậy r giúp vs :33 1 câu cx đc nhé :v toàn giải pt hết nhé1) 4x^2+left(8x-4right)sqrt{x}-13x+2sqrt{2x^2+5x-3}.2) left(5x+8right)sqrt{2x-1}+7xsqrt{x+3}9x+18-left(x+26right)sqrt{x-1}3) sqrt[3]{3x+1}+sqrt[3]{5-x}+sqrt[3]{2x-9}-sqrt[3]{4x-3}04) left(x+17right)sqrt{4-x}+left(20-xright)sqrt{x+1}-9sqrt{4-x}.sqrt{x+1}36
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Ai dậy r giúp vs :33 1 câu cx đc nhé :v toàn giải pt hết nhé
1) \(4x^2+\left(8x-4\right)\sqrt{x}-1=3x+2\sqrt{2x^2+5x-3}.\)
2) \(\left(5x+8\right)\sqrt{2x-1}+7x\sqrt{x+3}=9x+18-\left(x+26\right)\sqrt{x-1}\)
3) \(\sqrt[3]{3x+1}+\sqrt[3]{5-x}+\sqrt[3]{2x-9}-\sqrt[3]{4x-3}=0\)
4) \(\left(x+17\right)\sqrt{4-x}+\left(20-x\right)\sqrt{x+1}-9\sqrt{4-x}.\sqrt{x+1}=36\)
\(\left(5\right)\sqrt{x+3-4\sqrt{x-1}}\sqrt{x+8+6\sqrt{x-1}}=5\)
\(\left(6\right)2x^2+3x+\sqrt{2x^2+3x+9}=33\)
\(\left(7\right)\sqrt{3x^2+6x+12}+\sqrt{5x^4-10x^2+30}=8\)
\(\left(8\right)x+y+z+8=2\sqrt{x-1}+4\sqrt{y-2}+6\sqrt{z-3}\)
a) x+sqrt{left(x-2right)^2}b) sqrt{left(x-3right)^2} -xc) x-sqrt{left(x-1right)^2}d) sqrt{m^2-6m+9} -2me) m-sqrt{m^2-2m+1}f) 2x-sqrt{4x^2+4x+1}g)sqrt{x^2-10x+25} -xh) dfrac{sqrt{x^2+10x+25}}{x^2-25}i) dfrac{sqrt{1-2m+m^2}}{m^2-1}
Đọc tiếp
a) x+\(\sqrt{\left(x-2\right)^2}\)
b) \(\sqrt{\left(x-3\right)^2}\) -x
c) x-\(\sqrt{\left(x-1\right)^2}\)
d) \(\sqrt{m^2-6m+9}\) -2m
e) m-\(\sqrt{m^2-2m+1}\)
f) 2x-\(\sqrt{4x^2+4x+1}\)
g)\(\sqrt{x^2-10x+25}\) -x
h) \(\dfrac{\sqrt{x^2+10x+25}}{x^2-25}\)
i) \(\dfrac{\sqrt{1-2m+m^2}}{m^2-1}\)