(5x-1)²+(5x+1)²-2(1-25x²)=25x²-10x+1+25x²+10x+1-2-50x²

                                          = 0

Lời giải:

$(5x-1)^2+(5x+1)^2-2(1-25x^2)$

$=(5x-1)^2+(5x+1)^2-2(1-5x)(1+5x)$

$=(5x-1)^2+(5x+1)^2+2(5x-1)(5x+1)$

$=(5x-1+5x+1)^2$

$=(10x)^2=100x^2$

Ta có : \(\left(5x-1\right)^2-2\left(1-25x^2\right)+\left(5x+1\right)^2\)

\(=\left(5x-1\right)^2+2\left(25x^2-1\right)+\left(5x+1\right)^2\)

\(=\left(5x-1\right)^2+2\left(5x-1\right)\left(5x+1\right)+\left(5x+1\right)^2\)

\(=\left(5x-1+5x+1\right)^2=\left(10x\right)^2=100x^2\)

a: \(\left(2x+3y\right)\left(x-2y\right)-\dfrac{\left(4x^3y-6x^2y^2-3xy^3\right)}{2xy}\)

\(=2x^2-4xy+3xy-6y^2-\dfrac{2xy\cdot\left(2x^2-3xy-1,5y^2\right)}{2xy}\)
\(=2x^2-xy-6y^2-2x^2+3xy+1,5y^2\)

\(=2xy-4,5y^2\)

b: \(\left(x-2\right)^3-x\left(x+1\right)\left(x-1\right)-\left(3x-1\right)\left(3x-2\right)\)

\(=x^3-6x^2+12x-8-x\left(x^2-1\right)-\left(9x^2-6x-3x+2\right)\)

\(=x^3-6x^2+12x-8-x^3+x-9x^2+9x-2\)

\(=-15x^2+22x-10\)

A=(ghi lại biieur thức)

2A=2+1+1/2+1/2^2+….+1/2^2011

2A-A=A=(2+1+1/2+1/2^2+….+1/2^2011)-(1+1/2+1/2^2+...+1/2^2012)

A=2-1/2^2012

1/2 A= 1/2+1/2^2+1/2^3+1/2^4+...........+1/2^2013

=>A-1/2A= 1 -1/2^2013

=>1/2A=1 -1/2^2013

=>A=(1 - 1/2^2013) : 1/2

I don't know .

2A = 2 + 1 + 1/2 + 1/2² + 1/2³ + ... + 1/2²⁰¹¹

mà A = 1 + 1/2 + 1/2² + 1/2³ + ... + 1/2²⁰¹²

2A - A = 2 - 1/2²⁰¹²

A = 2 - 1/2²⁰¹²

Ta có A=1+1/2+1/2^2+1/2^3+........+1/2^2012

=>2A=2+1+1/2+1/2^2+.......+1/2^2011

=>2A-A=(2+1+1/2+1/2^2+.....+1/2^2011)-(1+1/2+1+1/2^2+1/2^3+.....+1/2^2012)

=>A=\(2-\frac{1}{2^{2012}}\)

\(A=\frac{2^{2013-1}}{2^{2012}}\)

A=đã cho.

1/2*A=1/2+1/2^2+1/2^3+...+1/2^2012+1/2^2013.

A-1/2*A=1-1/2^2013(khử).

1/2*A=1-1/2^2013.

A=2*(1-1/2^2013).

A=2-2/2^2013.

A=2-1/2^2012.

2A=2+1+1/2+1/2^2+1/2^3+...+1/2^2011
2A-A=(2+1+1/2+1/2^2+1/2^3+...+1/2^2011)-(1+1/2+1/2^2+1/2^3+...+1/2^2012)
A=2-2/2012
k cho mik nhé

1+1/2012

\(A=1+\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{2012}}\)

\(\frac{1}{2}A=\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+\frac{1}{2^4}+...+\frac{1}{2^{2013}}\)

\(\frac{1}{2}A-A=\left(\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+\frac{1}{2^4}+...+\frac{1}{2^{2013}}\right)-\left(1+\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{2012}}\right)\)

\(-\frac{1}{2}A=\frac{1}{2^{2013}}-1\)

\(A=\frac{\frac{1}{2^{2013}}-1}{2}\)

A = 1+1/2+1/2^2+1/2^3+.....+1/2^2012

2A= 2. (1+1/2+1/22+1/23+.....+1/22012)

2A= 2 + 1 + 1/2 + 1/22 + 1/23 + ...+ 1/22011

2A - A= (2 + 1 + 1/2 + 1/22 + 1/23+ ...+ 1/22011) - (1+1/2+1/22+1/23+.....+1/22012)

1A= 2 + 1 + 1/2 + 1/22 + 1/23 + ...+ 1/22011 - 1-1/2-1/22+1/23+.....+1/22012

1A= 2 - 1/22012

A= 2-1/22012

A= 2 - 1/22012

số mũ nữa nha

\(A=1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{2012}}\)

\(2A=2+1+\frac{1}{2}+...+\frac{1}{2^{2011}}\)

\(2A-A=\left(2+1+\frac{1}{2}+...+\frac{1}{2^{2011}}\right)-\left(1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{2012}}\right)\)

\(A=2-\frac{1}{2^{2012}}\)

A=2- 1/2^2012

a: \(=\sqrt{3}-1-\sqrt{3}=-1\)

b: \(=2\sqrt{3}-10\sqrt{3}+4\sqrt{3}=-4\sqrt{3}\)