Rut gon
\(\sqrt{4x^2-4x+1}+\sqrt{4x^2+4x+1}\)
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\(C=\dfrac{\sqrt{\dfrac{4x^2+4x+1}{x}}}{\sqrt{x}\cdot\left|2x^2-x-1\right|}=\dfrac{\left|2x+1\right|}{\sqrt{x}}\cdot\dfrac{1}{\sqrt{x}\cdot\left|\left(x-1\right)\left(2x+1\right)\right|}\)
\(=\dfrac{1}{x\left|x-1\right|}\)
\(A=\left(4x+5\right)^2-\left(3x-7\right)^2-\left(4x-1\right)\left(4x+1\right)\)
\(=\left(4x\right)^2+2.4x.5+5^2-\left[\left(3x\right)^2-2.3x.7+7^2\right]-\left[\left(4x\right)^2-1^2\right]\)
\(=16x^2+40x+25-\left(9x^2-42x+49\right)-\left(16x^2-1\right)\)
\(=16x^2+40x+25-9x^2+42x-49-16x^2+1=-9x^2+82x-23\)
A=(4x+5)2-(3x-7)2-(4x-1)(4x+1)
=16x2+40x+25-9x2+42x-49-16x2+1
=(16x2-9x2-16x2)+(40x+42x)+(25-49+1)
=-9x2+82x-23
\(\left(\frac{\sqrt{x}-4x}{1-4x}-1\right):\left(\frac{1+2x}{1-4x}-\frac{2\sqrt{x}}{2\sqrt{x}-1}-1\right)\left(ĐK:0\le x\ne\frac{1}{4}\right)\)
\(=\frac{\sqrt{x}-4x+4x-1}{1-4x}:\frac{\left(1+2x\right)+2\sqrt{x}\left(1+2\sqrt{x}\right)+4x-1}{1-4x}\)
\(=\frac{\sqrt{x}-1}{1-4x}.\frac{1-4x}{10x+2\sqrt{x}}=\frac{\sqrt{x}-1}{2\sqrt{x}\left(5\sqrt{x}+1\right)}\)
\(=\frac{\left(x+1\right)^2}{\left(x-1\right)^2}:\frac{2\left(x+1\right)^2}{4\left(x-1\right)^2}=\frac{\left(x+1\right)^2}{\left(x-1\right)^2}.\frac{4\left(x-1\right)^2}{2\left(x+1\right)^2}=2\)
( 4x-1)3+(4x-3)(16x2+3)
=64x3-48x2+12x-1+64x3+12x-48x2-9
=128x3-96x2+24x-10
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