\(\sqrt{10-2\sqrt{21}}+\sqrt{10+2\sqrt{21}}\)

\(=\sqrt{7-2\sqrt{21}+3}+\sqrt{7+2\sqrt{21}+3}\)

\(=\sqrt{\left(\sqrt{7}\right)^2-2.\sqrt{7}.\sqrt{3}+\left(\sqrt{3}\right)^2}+\sqrt{\left(\sqrt{7}\right)^2+2.\sqrt{7}.\sqrt{3}+\left(\sqrt{3}\right)^2}\)

\(=\sqrt{\left(\sqrt{7}-\sqrt{3}\right)^2}+\sqrt{\left(\sqrt{7}+\sqrt{3}\right)^2}\)

\(=\left|\sqrt{7}-\sqrt{3}\right|+\left|\sqrt{7}+\sqrt{3}\right|\)

\(=\sqrt{7}-\sqrt{3}+\sqrt{7}+\sqrt{3}\)

\(=\sqrt{7}+\sqrt{7}=2\sqrt{7}\)

Ta có: \(\sqrt{10-2\sqrt{21}}+\sqrt{10+2\sqrt{21}}\)

\(=\sqrt{7}-\sqrt{3}+\sqrt{7}+\sqrt{3}\)

\(=2\sqrt{7}\)

đặt \(A=\sqrt{10-2\sqrt{21}}+\sqrt{10+2\sqrt{21}}\)

\(=>A^2=10-2\sqrt{21}+10+2\sqrt{21}+2\sqrt{\left(10-2\sqrt{21}\right)\left(10+2\sqrt{21}\right)}\)

\(=>A^2=20+2\sqrt{10^2-\left(2\sqrt{21}\right)^2}=20+2\sqrt{16}=20+2.4=28\)

\(=>A=\sqrt{28}=2\sqrt{7}\)

\(=\sqrt{7-2\sqrt{21}+3}+\sqrt{7+2\sqrt{21}+3}\)

\(=\sqrt{\sqrt{7}^2-2\sqrt{7}.\sqrt{3}+\sqrt{3}^2}+\sqrt{\sqrt{7}^2+2\sqrt{7}.\sqrt{3}+\sqrt{3}^2}\)

\(=\sqrt{\left(\sqrt{7}-\sqrt{3}\right)^2}+\sqrt{\left(\sqrt{7}+\sqrt{3}\right)^2}\)

\(=\left|\sqrt{7}-\sqrt{3}\right|+\left|\sqrt{7}+\sqrt{3}\right|\)

\(=\sqrt{7}-\sqrt{3}+\sqrt{7}+\sqrt{3}\)

\(=2\sqrt{7}\)

\(\sqrt{10-2\sqrt{21}}+\sqrt{10+2\sqrt{21}}\)

\(=\sqrt{7}-\sqrt{3}+\sqrt{7}+\sqrt{3}\)

\(=2\sqrt{7}\)

\(\sqrt{10-2\sqrt{7}}+\sqrt{10+2\sqrt{21}}\)

\(=\sqrt{3-2\sqrt{7}+7}+\sqrt{3+2\sqrt{21}+7}\) 

\(=\sqrt{\sqrt{3}^2-2\sqrt{3}.\sqrt{7}+\sqrt{7}^2}+\sqrt{\sqrt{3}^2+2\sqrt{3}.\sqrt{7}+\sqrt{7}^2}\)

\(=\sqrt{\left(\sqrt{3}-\sqrt{7}\right)^2}+\sqrt{\left(\sqrt{3}+\sqrt{7}\right)^2}\)

\(=\left|\sqrt{3}-\sqrt{7}\right|+\left|\sqrt{3}+\sqrt{7}\right|\)

\(=\sqrt{7}-\sqrt{3}+\sqrt{3}+\sqrt{7}=2\sqrt{7}\)

`A = x/21 + y/21 + z/21.`

`= (x+y+z)/21 = 42/21 = 2`.

Vậy `A =2.`

Ta có:

A= 1/1.3 + 1/3.5 + .....+ 1/5.7 +......+ 1/19.21

2.A = 2/1.3 + 2/3.5 + 2/5.7 +...+ 2/19.21

2.A=  1- 1/3+ 1/3- 1/5+ 1/5- 1/7+............+ 1/19 - 1/21

2.A= 1- 1/21

2.A = 20/21

A= 20/21 : 2

A = 10/21

=> D

=>A mk nhầm

xl nhé hnay nt hiều quá 100 lần r lên k nt đc rất xl

A = \(\frac{-5x}{21}\)+  \(\frac{-5y}{21}\)+ \(\frac{-5x}{21}\)

    = \(\frac{\left(-5x\right)+\left(-5y\right)+\left(-5x\right)}{21}\)

    vì x + y là số dõi của z 

=> x + y + z = 0 

=> \(\frac{5.\left(x+y+z\right)}{21}\)

= \(\frac{-5}{21}\).  0 = 0 

=> A = 0 

hok tốt !

Thay -z=x+y vào biểu thức A ta có A=-5x/21+(-5y/21)+[5(x+y)/21] =>-5x/21 +(-5y/21)+(5x+5y)/21=>-5x/21+(-5y/21)+5x/21+5y/21 => A = 0

Theo đầu bài ta có:
\(A=\frac{-5x}{21}+\frac{-5y}{21}+\frac{-5z}{21}\)
\(=\frac{-5x+-5y+-5z}{21}\)
\(=\frac{-5\left(x+y+z\right)}{21}\)
\(=\frac{-5\left(-z+z\right)}{21}\)
\(=\frac{-5\cdot0}{21}\)
\(=\frac{0}{21}=0\)

\(A=\frac{-5x}{21}+\frac{-5y}{21}+\frac{-5z}{21}\)

=>\(A=\frac{\left(-5x\right)+\left(-5y\right)+\left(-5z\right)}{21}\)

=>\(A=\frac{\left(-5\right)\left(x+y+z\right)}{21}\)

=>\(A=\frac{\left(-5\right)\left(-z+z\right)}{21}\)

=>\(A=\frac{\left(-5\right).0}{21}\)

=>\(A=\frac{0}{21}\)

=>A=0