The output value of a factory in January was 500000 yuan. After adopting advanced technology, the output value in February was 20% higher than that in January, and the output value in April was 1014000 yuan Ask the average growth rate in March and April!

The output value of a factory in January was 500000 yuan. After adopting advanced technology, the output value in February was 20% higher than that in January, and the output value in April was 1014000 yuan Ask the average growth rate in March and April!

Let the average growth rate in March and April be X
The output value in February was 50 * (1 + 20%) = 60
Therefore, 60 * (1 + x) ^ 2 = 101.4
Therefore, x = 30%

Solve a junior high school mathematics problem. Use binary linear equation to solve
A unit walked in the desert for four hours on the first day, and five hours on the second day, with a total of 98km on the two days. The first day was 2km less than the second day. What's the average speed of the two days?

One day x, two days y
4x+5y=98
5y-4x=2
The solution is y = 10km
x=12km

To solve the equations: X − 4Y = 1x2 − XY + 2 = 2Y2 + 2

X − 4Y = 1 (1) x2 − XY + 2 = 2Y2 + 2 (2) change (1) into: x = 1 + 4Y, substitute (2) to get: (1 + 4Y) 2 - (1 + 4Y) y-2y2 = 0, that is 10y2 + 7Y + 1 = 0, the solution is: Y1 = − 12, y2 = − 15, X1 = - 1, X2 = 15, the solution of the original equations is: x = − 1y = − 12, x = 15y = − 15

Application of quadratic equation of two variables
1. A clothing factory produces a batch of costumes for the school art troupe. The total cost is 3000 yuan, and the price is 30 yuan per set. There are 24 poor students in the family who supply them for free. After accounting, the cost of these 24 sets of costumes is exactly the profit of the original production of these costumes. So how many sets of costumes are there in total?
2. The diameter of a well is 2 meters, and a bamboo pole is used to extend into the bottom of the well. The bamboo pole is 0.5 meters higher than the wellhead. If the bamboo pole is extended into the wellhead obliquely, and the bamboo pole is just level with the wellhead, how many meters is the depth of the well?

(1) . there are x sets in total
3000 / X × 24 = 30x-3000 72000 / x = 30x-3000 30x ^ 2-3000x = 72000 x ^ 2-100x-2400 = 0 (x-50) ^ 2 = 4900 x-50 = 70 or - 70, then X1 = 120, X2 = 20, and because the meaning of the title x should be greater than 24, so x = 120
(2) If the well depth is x m, then x ^ 2 = (x 0.5) ^ 2-2 ^ 2 - x = - 3.75, x = 3.75