Cho M=\(2x-3-\sqrt{4x^2-12x+9}\)
a) Rut gon M
b) Tinh M khi x=\(x=\frac{5}{2};x=\frac{-1}{5}\)
Những câu hỏi liên quan
Cho A=\(4x-\sqrt{8}-\frac{\sqrt{x^3+2x^2}}{\sqrt{x+2}}\)
a) Rut gon A khi x >2
b)Tinh A khi x=\(\sqrt{-2}\)
câu b) \(\sqrt{-2}\) không xác định
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a) \(A=4x-\sqrt{8}-\frac{\sqrt{x^3+2x^2}}{\sqrt{x+2}}\)
\(=4x-\sqrt{8}-\frac{\sqrt{x^2\left(x+2\right)}}{\sqrt{x+2}}=4x-\sqrt{8}-x=3x-\sqrt{8}\)
b) \(x=\sqrt{-2}\) (không thỏa mãn)
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B1: rut gon bieu thuc
a, (x+y)^2-4(x-y)^2
b, 2(x-y)(x+y)+(x+y)^2+(x-y)^2
B2: tim X
a, (2X-1)^2-4(X+2)^2=9
b, 3(X-1)^2-3X(X-5)=21
B3: Cho bieu thuc
M=(x+3)^3-(x-1)^3+12x(x-1)
a, Rut gon bieu thuc tren
b, Tinh gia tri M tai x=-2/3
c, Tim x de M=16
1)a)=>x2+y2+2xy-4(x2-y2-2xy)
=>x2+y2+2xy-4.x2+4y2+8xy
=>-3.x2+5y2+10xy
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Giúp mình nhé!!
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) \(B=\dfrac{1}{2}\sqrt{x^2}+\sqrt{x^2-2x+1}\)
cho A=\(\frac{x+7}{\sqrt{x}}\); B=\(\frac{\sqrt{x}}{\sqrt{x+3}}\)+\(\frac{2\sqrt{x-1}}{\sqrt{x-3}}\)-\(\frac{2x-\sqrt{x-3}}{x-9}\)
a, tinh A khi x=16
b, rut gon B
c,tim Min cua p=A+1/B
Cho A = \(\frac{3\sqrt{x}-3}{x\sqrt{x}-2x+2\sqrt{x}-1}-\frac{4x\sqrt{x}-4}{x^3-1}\)(x>1). Rut gon A va tim x de A=1
Cho bieu thuc:
P=\(\frac{1}{\sqrt{x}+2}-\frac{5}{x-\sqrt{x}-6}-\frac{\sqrt{x}-2}{3-\sqrt{x}}\)
a. Rut gon bieu thuc P
b.Tim GTLN cua P sau khi rut gon
đk: x>=0; x khác 3
a) \(P=\frac{\sqrt{x}-3}{\left(\sqrt{x}+2\right)\left(\sqrt{x}-3\right)}-\frac{5}{\left(\sqrt{x}+2\right)\left(\sqrt{x}-3\right)}+\frac{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}{\sqrt{x}-3}=\frac{\sqrt{x}-3-5+x-4}{\left(\sqrt{x}+2\right)\left(\sqrt{x}-3\right)}=\frac{x+\sqrt{x}-12}{\left(\sqrt{x}+2\right)\left(\sqrt{x}-3\right)}\)
\(P=\frac{\left(\sqrt{x}+4\right)\left(\sqrt{x}-3\right)}{\left(\sqrt{x}+2\right)\left(\sqrt{x}-3\right)}=\frac{\sqrt{x}+4}{\sqrt{x}+2}\)
b) \(P=\frac{\sqrt{x}+2+2}{\sqrt{x}+2}=1+\frac{2}{\sqrt{x}+2}\)
ta có: \(x\ge0\Rightarrow\sqrt{x}\ge0\Leftrightarrow\sqrt{x}+2\ge2\Leftrightarrow\frac{2}{\sqrt{x}+2}\le1\Leftrightarrow1+\frac{2}{\sqrt{x}+2}\le2\Rightarrow MaxP=2\Rightarrow x=0\)
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M=(x2-2x/2x2+8 - 2x2/8-4x+2x2-x3)*(1-1/x-2/x2)
a, Rut gon M
b,Tinh M voi x=1/2
c,tinh x de M<0
cho P=\(\left(2-\frac{\sqrt{x}-1}{2\sqrt{x}-3}\right):\left(\frac{6\sqrt{x}+1}{2x-\sqrt{x}-3}+\frac{\sqrt{x}}{\sqrt{x}+1}\right)\\ \)
a, rut gon P
b, tinh gia tri cua P khi \(x=\frac{3-2\sqrt{2}}{4}\)
c, so sanh P voi \(\frac{3}{2}\)
Cho B=\(\sqrt{\frac{\left(x-2\right)^4}{\left(3-x\right)^2}}+\frac{x^2+1}{x-3}\)
a)Rut gon B khi x<3
b)Tinh B khi x=0,5
a) \(B=\sqrt{\frac{\left(x-2\right)^4}{\left(3-x\right)^2}}+\frac{x^2+1}{x-3}=\frac{\left(x-2\right)^2}{3-x}+\frac{x^2+1}{x-3}\\ =\frac{-\left(x-2\right)^2+x^2+1}{x-3}=\frac{-x^2+4x-4+x^2+1}{x-3}=\frac{4x-3}{x-3}\)
b) khi x=0,5 thì
\(B=\frac{4\cdot0,5-3}{0,5-3}=\frac{2}{5}\)
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