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\(=\frac{\left(x+1\right)^2}{\left(x-1\right)^2}:\frac{2\left(x+1\right)^2}{4\left(x-1\right)^2}=\frac{\left(x+1\right)^2}{\left(x-1\right)^2}.\frac{4\left(x-1\right)^2}{2\left(x+1\right)^2}=2\)
ĐK: x ≥ 0,5
\(\sqrt{4x^2-4x+1}+\sqrt{4x^2+4x-1}\)
=\(\sqrt{\left(2x-1\right)^2}+\sqrt{\left(2x+1\right)^2}\)
=\(\left|2x-1\right|+\left|2x+1\right|\)
= 2x-1+2x+1
= 4x
a)
\(M=2+\sqrt{\left(2x\right)^2-2.2x.3+3^2}\)
\(\Rightarrow M=2+\sqrt{\left(2x-3\right)^2}\)
\(\Rightarrow M=2+2x-3\)
\(\Rightarrow M=2x-1\)
b)
(+) x=5/2
=> \(M=2.\frac{5}{2}-1=5-1=4\)
(+) x= - 1/5
=> \(M=2.\frac{\left(-1\right)}{5}-1=-\frac{2}{5}-1=-\frac{7}{5}\)
\(C=\dfrac{\sqrt{\dfrac{4x^2+4x+1}{x}}}{\sqrt{x}\cdot\left|2x^2-x-1\right|}=\dfrac{\left|2x+1\right|}{\sqrt{x}}\cdot\dfrac{1}{\sqrt{x}\cdot\left|\left(x-1\right)\left(2x+1\right)\right|}\)
\(=\dfrac{1}{x\left|x-1\right|}\)
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)
1)
a)
\(\sqrt{11-6\sqrt{2}}=\sqrt{2-2.3.\sqrt{2}+9}=\left|\sqrt{2}-3\right|=3-\sqrt{2}\)
\(A=3-\sqrt{2}+3+\sqrt{2}=6\)
b)
\(B^2=24+2\sqrt{12^2-4.11}=24+2\sqrt{100}=24+20=44\)
\(B=\sqrt{44}=2\sqrt{11}\)
N=2(2x + 5 )^2 - 3(1 + 4x )(1 - 4x)
= 2 (4x^2 + 20x + 25) - 3(1 - 16x^2)
= 8x^2 + 40x + 50 - 3 + 48x^2
= 56x^2 + 40x - 47
(.....????!!!!!!.....)