\(\frac{2}{x^2y^2}\sqrt{\frac{3\left(x+y\right)^2}{2}}\left(x\ge0;y\ge0;x\ne y\right)\)
\(=\frac{\left|x+y\right|}{x^2-y^2}\sqrt{\frac{3.2^2}{2}}\)
\(=\frac{\left(x+y\right)}{\left(x-y\right)\left(x+y\right)}\sqrt{6}\)
\(=\frac{1}{x-y}\sqrt{6}\)
Các câu hỏi tương tự
B1 Rút gọn
a)\(\sqrt{6+2\sqrt{5}}-\sqrt{29-12\sqrt{2}}\)
b)\(\frac{2}{x^2y^2}\sqrt{\frac{3\left(x+y\right)^2}{2}}\left(x\ge0;y\ge0;x\ne y\right)\)
c)\(\frac{2}{2a-1}\sqrt{5a^2\left(1-4a+4a^2\right)}\left(a>\frac{1}{2}\right)\)
B2 giải pt
\(\sqrt{3-x}+3\sqrt{12-4x}-5\sqrt{48-16x}=-39\)
HELP ME!!!!
Rút gọn:a)2sqrt{3x}-4sqrt{3x}+27-2sqrt{3x}(xge0)b)3sqrt{2x}-5sqrt{8x}+7sqrt{8x}+28left(xge0right)c)frac{2}{x^2-y^2}sqrt{frac{3left(x+yright)^2}{2}}left(xge0,yge0,xne yright)d)frac{2}{2a-1}sqrt{5a^2left(1-4a+4a^2right)}
Đọc tiếp
Rút gọn:
a)\(2\sqrt{3x}-4\sqrt{3x}\)+\(27-2\sqrt{3x}\)(\(x\ge0\))
b)\(3\sqrt{2x}-5\sqrt{8x}\)+\(7\sqrt{8x}+28\)\(\left(x\ge0\right)\)
c)\(\frac{2}{x^2-y^2}\sqrt{\frac{3\left(x+y\right)^2}{2}}\)\(\left(x\ge0,y\ge0,x\ne y\right)\)
d)\(\frac{2}{2a-1}\sqrt{5a^2\left(1-4a+4a^2\right)}\)
Rút gọn
a)\(\frac{x\sqrt{x}+y\sqrt{y}}{\sqrt{x}+\sqrt{y}}\)(\(x\ge0;y\ge0;x\ne y\))
b)\(\frac{x\sqrt{x}-8}{x+2\sqrt{x}+4}\)\(\left(x\ge0\right)\)
Rút gọna)sqrt{75}+sqrt{75}-sqrt{192}b)3sqrt{2x}-5sqrt{2x}-5sqrt{2x}+9-6sqrt{2x}left(x0right)c)3sqrt{2x}-4sqrt{8x}-5sqrt{50x}left(x0right)d)frac{1}{x^2-y^2}.sqrt{frac{2left(x+yright)^2}{3}}left(xge0;yge0;xne yright)e)left(3sqrt{2}+sqrt{3}right).sqrt{2}sqrt{54}f)2sqrt{21}-left(sqrt{28}+sqrt{12}-sqrt{7}right).sqrt{7}
Đọc tiếp
Rút gọn
a)\(\sqrt{75}+\sqrt{75}-\)\(\sqrt{192}\)
b)3\(\sqrt{2x}-5\sqrt{2x}-5\sqrt{2x}+9-6\sqrt{2x}\left(x>0\right)\)
c)3\(\sqrt{2x}-4\sqrt{8x}-5\sqrt{50x}\left(x>0\right)\)
d)\(\frac{1}{x^2-y^2}.\sqrt{\frac{2\left(x+y\right)^2}{3}}\left(x\ge0;y\ge0;x\ne y\right)\)
e)\(\left(3\sqrt{2}+\sqrt{3}\right).\sqrt{2}\sqrt{54}\)
f)\(2\sqrt{21}-\left(\sqrt{28}+\sqrt{12}-\sqrt{7}\right).\sqrt{7}\)
Cho A = \(\left(\frac{x-y}{x-\sqrt{y}}-\frac{x\sqrt{x}-y\sqrt{y}}{x-y}\right):\left(\frac{\left(\sqrt{x}-\sqrt{y}\right)^2+\sqrt{xy}}{\sqrt{x}+\sqrt{y}}\right)\)
a) Rút gọn A
b) CM: \(A\ge0\)
Rút gọna)3sqrt{40sqrt{12}}+4sqrt{sqrt{75}}-5sqrt{5sqrt{48}}b)sqrt{8sqrt{3}}+3sqrt{20sqrt{3}}-2sqrt{45sqrt{3}}c)left(sqrt{x}-1right).left(x+sqrt{x}+1right)left(xge0;yge0right)d)left(sqrt{x}+1right)left(x+1-sqrt{x}right)left(xge0;yge0right)e)left(sqrt{x}+yright).left(x+y^2-ysqrt{2}right)left(xge0;yge0right)
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Rút gọn
a)\(3\sqrt{40\sqrt{12}}+4\sqrt{\sqrt{75}}-5\)\(\sqrt{5\sqrt{48}}\)
b)\(\sqrt{8\sqrt{3}}+3\sqrt{20\sqrt{3}}-2\sqrt{45\sqrt{3}}\)
c)\(\left(\sqrt{x}-1\right).\left(x+\sqrt{x}+1\right)\left(x\ge0;y\ge0\right)\)
d)\(\left(\sqrt{x}+1\right)\left(x+1-\sqrt{x}\right)\left(x\ge0;y\ge0\right)\)
e)\(\left(\sqrt{x}+y\right).\left(x+y^2-y\sqrt{2}\right)\left(x\ge0;y\ge0\right)\)
Rút gọna) sqrt{75}+sqrt{48}-sqrt{192}b)3sqrt{2x}-5sqrt{2x}-5sqrt{2x}9-6sqrt{2x}left(x0right)c)3sqrt{2x}-4sqrt{8x}-5sqrt{50x}left(x0right)d)frac{1}{x^2-y^2}.sqrt{frac{2left(x+yright)^2}{3}}left(xge0;yge0;xne yright)e)left(3sqrt{2}+sqrt{3}right).sqrt{2}-sqrt{54}f)2sqrt{21}-left(sqrt{28}+sqrt{12}-sqrt{7}right).sqrt{7}
Đọc tiếp
Rút gọn
a) \(\sqrt{75}+\sqrt{48}-\)\(\sqrt{192}\)
b)\(3\sqrt{2x}-5\sqrt{2x}-5\sqrt{2x}=9-6\sqrt{2x}\left(x>0\right)\)
c)\(3\sqrt{2x}-4\sqrt{8x}-5\sqrt{50x}\left(x>0\right)\)
d)\(\frac{1}{x^2-y^2}.\sqrt{\frac{2\left(x+y\right)^2}{3}}\left(x\ge0;y\ge0;x\ne y\right)\)
e)\(\left(3\sqrt{2}+\sqrt{3}\right).\sqrt{2}-\sqrt{54}\)
f)\(2\sqrt{21}-\left(\sqrt{28}+\sqrt{12}-\sqrt{7}\right).\sqrt{7}\)
Cho \(P=\frac{\left(\sqrt{x}-\sqrt{y}\right)^2+\sqrt{xy}}{\sqrt{x}+\sqrt{y}}\div\left(\frac{x-y}{\sqrt{x}-\sqrt{y}}+\frac{x\sqrt{x}-y\sqrt{y}}{y-x}\right)\)Với \(x,y\ge0;x\ne y\)
a) Rút gọn \(P\)
b) CMR: \(P>1\)
Rút gọn:
a,\(\frac{\left(x\sqrt{y}+y\sqrt{x}\right).\left(\sqrt{x}-\sqrt{y}\right)}{\sqrt{xy}}\left(x,y>0\right)\)
b,\(\frac{\sqrt{x^3}-1}{\sqrt{x}-1}\left(x\ge0;x\ne1\right)\)
c,\(\sqrt{x+2\sqrt{2x-4}}+\sqrt{x-2\sqrt{2x-4}}\)