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

\(\dfrac{x+1}{59}+\dfrac{x+3}{57}+\dfrac{x+5}{55}=\dfrac{x+7}{53}+\dfrac{x+9}{51}+\dfrac{x+11}{49}\)

\(< =>\dfrac{x+1}{59}+1+\dfrac{x+3}{57}+1+\dfrac{x+5}{55}+1=\dfrac{x+7}{53}+1+\dfrac{x+9}{51}+1+\dfrac{x+11}{49}+1\)

\(< =>\dfrac{x+60}{59}+\dfrac{x+60}{57}+\dfrac{x+60}{55}=\dfrac{x+60}{53}+\dfrac{x+60}{51}+\dfrac{x+60}{49}\)

\(< =>\left(x+60\right)\left(\dfrac{1}{59}+\dfrac{1}{57}+\dfrac{1}{55}-\dfrac{1}{53}-\dfrac{1}{51}-\dfrac{1}{49}\right)=0\\ < =>x+60=0\\ < =>x=-60\)

Ta có : \(\dfrac{x+1}{59}+\dfrac{x+3}{57}+\dfrac{x+5}{55}=\dfrac{x+7}{53}+\dfrac{x+9}{51}+\dfrac{x+11}{49}\)

\(\Leftrightarrow\dfrac{x+1}{59}+\dfrac{x+3}{57}+\dfrac{x+5}{55}+3\text{=}\dfrac{x+7}{53}+\dfrac{x+9}{51}+\dfrac{x+11}{49}+3\)

\(\Leftrightarrow\left(\dfrac{x+1}{59}+1\right)+\left(\dfrac{x+3}{57}+1\right)+\left(\dfrac{x+5}{55}+1\right)\text{=}\left(\dfrac{x+7}{53}+1\right)+\left(\dfrac{x+9}{51}+1\right)+\left(\dfrac{x+11}{49}+1\right)\)

\(\Leftrightarrow\left(\dfrac{x+1}{59}+1\right)+\left(\dfrac{x+3}{57}+1\right)+\left(\dfrac{x+5}{55}+1\right)\text{=}\left(\dfrac{x+7}{53}+1\right)+\left(\dfrac{x+9}{51}+1\right)+\left(\dfrac{x+11}{49}+1\right)\)

\(\Leftrightarrow\dfrac{x+60}{59}+\dfrac{x+60}{57}+\dfrac{x+60}{55}\text{=}\dfrac{x+60}{53}+\dfrac{x+60}{51}+\dfrac{x+60}{49}\)

\(\Leftrightarrow\dfrac{x+60}{59}+\dfrac{x+60}{57}+\dfrac{x+60}{55}-\dfrac{x+60}{53}-\dfrac{x+60}{51}-\dfrac{x-60}{49}\text{=}0\)

\(\Leftrightarrow\left(x+60\right)\left(\dfrac{1}{59}+\dfrac{1}{57}+\dfrac{1}{55}-\dfrac{1}{53}-\dfrac{1}{51}-\dfrac{1}{49}\right)\text{=}0\)

\(Do\) \(\dfrac{1}{59}+\dfrac{1}{57}+\dfrac{1}{55}-\dfrac{1}{53}-\dfrac{1}{51}-\dfrac{1}{49}\ne0\)

\(\Leftrightarrow\left(x+60\right)\text{=}0\)

\(x\text{=}-60\)

\(Vậy...\)

đây mà là toán lớp 6

Mình chỉ biết làm phần cuối thôi :

​1 + 2 + 3 + 4 + .... + 50

​Số lượng số hạng là :

​( 50 - 1 ) : 1 + 1 = 50 ( số )

​Tổng là :

​( 50 + 1 ) x 50 : 2 = 1275

​Đáp số : 1275

​

​

​

Số số hạng của dãy trên là : 

( 59 - 2 ) : 3 + 1 = 20 ( sốm hạng )

Tổng dãy trên là :

( 59 + 2 ) x 20 : 2 = 610

số số hạng :

(59 - 2) : 3 + 1 = 20 (số hạng)

tổng :

(59 + 2).20 : 2 = 610

Khiếp

2 . 53 . 27 + 6 . 9 . 87 - 3 . 18 . 40 
= 2. 53 . 9 . 3 + 2. 3 .9 .87 - 3 .2 .9 .40
= 54.53+54.87-54.40
=54(53+87-40)
=54. 100=5400

12 . 25 + 29 . 25 + 59 . 25 
= 25 . ( 12+29+59)
=25 . 90
=2250

43 . 37 + 93 . 43 + 57 . 61 + 69 . 57 
= 43.(37+93)+57(61+69)
=43.130+57.130
=130.(43+57)
=130.100
=13 000

12 . 53 + 53 . 172 - 53 
=53(12+172-1)
=53.184
=9752

35 . 54 + 35 . 58 + 65 . 75 + 65 . 45 
=35(54+58)+65(75+45)
=35.112+65.120
=3920+7800
=11720

39 . 8 + 70 . 3 + 31 . 8 
=8(39+31)+70.3
=8.70+70.3
=70.(8+3)
=70.11
=770

\(\left(-59\right)\cdot\left(-43\right)-59\cdot53\)

\(=59\cdot43-59\cdot53\)

\(=59\cdot\left(43-53\right)\)

\(=59\cdot-10=-590\)

ket qua la 590

Số các số hạng là:

(41-5):3+1=13 (số)

Tổng là:

(41+5)x13:2=299

Đáp số:299