1711

cho xin vài tick nhé các bạn    Thanks

 Số các số hạng là:

(58 - 1) + 1 = 58 (số)

Tổng là:

(58 + 1) x 58 : 2 = 1711   

50) \(\sqrt{98-16\sqrt{3}}=4\sqrt{6}-\sqrt{2}\)

51) \(\sqrt{2-\sqrt{3}}=\dfrac{\sqrt{4-2\sqrt{3}}}{\sqrt{2}}=\dfrac{\sqrt{3}-1}{\sqrt{2}}=\dfrac{\sqrt{6}-\sqrt{2}}{2}\)

52) \(\sqrt{4+\sqrt{15}}=\dfrac{\sqrt{8+2\sqrt{15}}}{\sqrt{2}}=\dfrac{\sqrt{5}+\sqrt{3}}{\sqrt{2}}=\dfrac{\sqrt{10}+\sqrt{6}}{2}\)

53) \(\sqrt{5-\sqrt{21}}=\dfrac{\sqrt{10-2\sqrt{21}}}{\sqrt{2}}=\dfrac{\sqrt{14}-\sqrt{6}}{2}\)

54) \(\sqrt{6-\sqrt{35}}=\dfrac{\sqrt{12-2\sqrt{35}}}{\sqrt{2}}=\dfrac{\sqrt{14}-\sqrt{10}}{2}\)

55) \(\sqrt{2+\sqrt{3}}=\dfrac{\sqrt{4+2\sqrt{3}}}{\sqrt{2}}=\dfrac{\sqrt{6}+\sqrt{2}}{2}\)

56) \(\sqrt{4-\sqrt{15}}=\dfrac{\sqrt{8-2\sqrt{15}}}{\sqrt{2}}=\dfrac{\sqrt{10}-\sqrt{6}}{2}\)

Can bac 8

1+2+3-4-5-6+7+8+9+...+55+56+57-58-59-60

=(1+2+3-4-5-6)+(7+8+9-10-11-12)+.......+(55+56+57-58-59-60)

=(-9)+(-9)+......+(-9)

còn lại bạn làm theo cách tính tổng của dãy là đc

\(A=\left(157.57-99.57-57^2\right):57+57\)

\(=\left[\left(157-99\right).57-57^2\right]:57+57\)

\(=\left[58.57-57^2\right]:57+57\)

\(=\left[3306-3249\right]:57+57\)

\(=57:57+57\)

\(=1+57=58\)

Vậy....

\(B=\left[160.\left(730-700\right):2^4-4^2\right].13\)

\(=\left[160.30:16-16\right].13\)

\(=\left[4800:16-16\right].13\)

\(=\left(300-16\right).13\)

\(=284.13=3692\)

Vậy...

\(C=\left(3^2.17+3^2.38-55\right):\left(2^3.68-2^3.13\right)\)

\(=\left(9.17+9.38-55\right):\left(8.68-8.13\right)\)

\(=\left[9.\left(17+38\right)-55\right]:\left[8.\left(68-13\right)\right]\)

\(=\left[9.55-55\right]:\left[8.55\right]\)

\(=\left[8.55\right]:\left[8.55\right]\)

\(=1\)

Vậy...

\(D=2.51^2:17^2+\left(8.5^2-2^4-3^2\right):56+2009\)

\(=2.8+\left(8.25-16-9\right):56+2009\)

\(=18+\left(200-16-9\right):56+2009\)

\(=18+175:56+2009\)

\(=18+\dfrac{25}{8}+2009\)

\(=\dfrac{16241}{8}\)

Ta có:

1+2+3-4-5-6+7+8+9-..........+55+56+57-58-59-60

=(1+2+3-4-5-6)+(7+8+9-10-11-12)..........+(55+56+57-58-59-60)

=  -3+ (-3)+...+(-3)

---12 số------------

=(-3).12

=-36

Ta có: \(\dfrac{x-1}{59}+\dfrac{x-2}{58}+\dfrac{x-3}{57}=\dfrac{x-4}{56}+\dfrac{x-5}{55}+\dfrac{x-6}{54}\)

\(\Leftrightarrow\dfrac{x-60}{59}+\dfrac{x-60}{58}+\dfrac{x-60}{57}-\dfrac{x-60}{56}-\dfrac{x-60}{55}-\dfrac{x-60}{54}=0\)

\(\Leftrightarrow x-60=0\)

hay x=60

\(\left(\dfrac{x+1}{55}+\dfrac{x+2}{56}+\dfrac{x+3}{57}+\dfrac{x+4}{58}\right)-4=0\)

<=>\(\dfrac{x+1}{55}+\dfrac{x+2}{56}+\dfrac{x+3}{57}+\dfrac{x+4}{58}=4\)

<=>\(\dfrac{x+1}{55}-1+\dfrac{x+2}{56}-1+\dfrac{x+3}{57}+\dfrac{x+4}{58}-1=4-4\)

<=>\(\dfrac{x+1}{55}-\dfrac{55}{55}+\dfrac{x+2}{56}-\dfrac{56}{56}+\dfrac{x+3}{57}-\dfrac{57}{57}+\dfrac{x+4}{58}-\dfrac{58}{58}=0\)

<=>\(\dfrac{x-54}{55}+\dfrac{x-54}{56}+\dfrac{x-54}{57}+\dfrac{x-54}{58}=0\)

<=>\(\left(x-54\right)\left(\dfrac{1}{55}+\dfrac{1}{56}+\dfrac{1}{57}+\dfrac{1}{58}\right)=0\)

<=>x-54=0

<=>x=54

vậy phương trình có tập nghiệm là S={54}

ở dòng thứ 6 cậu thêm  \(\dfrac{1}{55}+\dfrac{1}{56}+\dfrac{1}{57}+\dfrac{1}{58}\ne0\) để giải thích nhé .

Xin lỗi mình làm hơi tắt nha !!!Còn 1 cách nữa ,nếu bạn muốn thì nói với mình nha !!

Ta có : \(\frac{x-1}{59}+\frac{x-2}{58}+\frac{x-3}{57}=\frac{x-4}{56}+\frac{x-5}{55}+\frac{x-6}{54}\)

\(\Leftrightarrow\frac{x}{59}+\frac{x}{58}+\frac{x}{57}-\frac{x}{56}-\frac{x}{55}-\frac{x}{54}=\frac{1}{59}+\frac{2}{58}+\frac{3}{57}-\frac{4}{56}-\frac{5}{55}-\frac{6}{54}\)

<=> x = 60 

Vậy x = 60

Bạn kiểm tra lại đề nhé. Chỗ

\(.....=\frac{x-4}{56}+\frac{x-5}{56}+\frac{x-6}{54}\)

a)  >

b) > 

c) >   

d) <