Change the following equation to a ratio of 1.5 × 6 = 3 × 10 2.3 / 1 × 12 = 8 × 2 / 1,

Change the following equation to a ratio of 1.5 × 6 = 3 × 10 2.3 / 1 × 12 = 8 × 2 / 1,

1.5×6=3×10
5:3=6:10
1 / 2.3 × 12 = 1 / 8 × 2
8:12=1/3 ：1/2

How to calculate the sum of numbers in each line of Yang Hui triangle
For example: Line 10. How can I quickly find the number of 10 lines and calculate the number of 10 lines and the result

Use the combination number formula
Line 10 I = C (10, I) = 10! / I! * (10-i)!
i!=1*2*3*4*5*6*7… i

How to use Yang Hui triangle to calculate (√ 3 + √ 2) ^ 6
Do not use a calculator

According to Yang Hui's Triangle:
1……………… n=0
1 1………… n=1
1 2 1………… n=2
1 3 3 1………… n=3
1 4 6 4 1………… n=4
1 5 10 10 5 1………… n=5
1 6 15 20 15 6 1………… n=6
Here we know that the coefficients of (√ 3 + √ 2) ^ 6 expansion are: 1,6,15,20,15,6,1
Then there are: 1 * (√ 3 ^ 6 * √ 2 ^ 0) + 6 * (√ 3 ^ 5 * √ 2 ^ 1) + 15 * (√ 3 ^ 4 * √ 2 ^ 2) + 20 * (√ 3 ^ 3 * √ 2 ^ 3) + 15 * (√ 3 ^ 2 * √ 2 ^ 4) + 6 * (√ 3 ^ 1 * √ 2 ^ 5) + (√ 3 ^ 0 * √ 2 ^ 6) = 27 + 54 √ 6 + 270 + 120 √ 6 + 180 + 24 √ 6 + 8 = 485 + 198 √ 6 = 969.99
The result is the same as that calculated by computer