How to solve binary quadratic equation

It has no formula for finding roots like quadratic equation of one variable,
It is mainly solved by elimination transformation,
If you can decompose a factor, it's easy to use special techniques such as factorization or substitution!

Solving quadratic equation of two variables
5x ^ 2-3xy + y ^ 2 / 2-2x + Y / 2 + 1 / 4 = 0, the value of Y

Here I come ~ ha ha! Multiply the equation by 4 times and it will be equal to 20x ＾ 2-12xy + 2Y ^ 2-8x + 2Y + 1 = 0. Divide it into 4x ^ 2-4xy + y ^ 2 + 16x ^ 2-8xy + y ^ 2-8x + 2Y + 1 = 0 and change it into (2x-y) ^ 2 + (4x-y) ^ 2-2 (4x-y) + 1 = 0 (2x-y) ^ 2 + (4x-y-1) ^ 2 = 0. Because both squares are greater than or equal to 0, so 1.2

Help to solve the maximum value of a quadratic equation
I've been working on a topic for a long time, but I can't make the last step
(cubic of 2m-quadratic of 8m + 8m-2) divided by (m-1)
It means the cubic power of M, not the cubic power of 2m
Find the maximum of this formula
Wrong, it's (cubic of 2m - quadratic of 8m + 8m - 2) divided by (square of M - M)

Original form
=[2（m^3-1）-8(m^2-m)]/(m-1)
=[2(m-1)(m^2+m+1)-8m(m-1)]/(m-1)
=2(m^2+m+1)-8m
=2m^2-6m+2
=2(m^2-3m+1)
=2(m^3-3m+9/4)-5/2
=2(m-3/2)^2-2.5
So the original formula has no maximum value, but a minimum value of - 2.5

What is the area of a trapezoid with an increase of 7 cm in the upper bottom and a decrease of 7 cm in the lower bottom

The area of this trapezoid has not changed

In the RT triangle ABC, C = 90 degrees, perimeter 60cm, and two right angle sides BC ratio AC + 5 ratio 12, find the value of s triangle ABC

Because of the right triangle, the ratio of three sides is 5:12:13. According to the perimeter, the length of two right sides is 10 24, and the area is 10 × 24 / 2 = 120

Look at the picture and guess the idiom "ten suns and snowflakes"

Ice and snow?

601 bus every 8 minutes, 608 bus every 12 minutes, 7 o'clock in the morning two bus at the same time, calculate the next time at the same time when? Please talk about it

Finding the least common multiple of 8 and 12 is 24. It starts at the same time in 24 minutes, that is, it starts at 7:24 for the second time

How many centimeters should a bridge with an actual length of 1200 meters be drawn on a plan with a scale of 1:20000?

1 mm in the figure is equal to 20000 mm in practice, that is 20 meters
Therefore, 1200 meters requires 60 mm and 6 cm on the plan

Famous sayings of mathematicians

1. Percentage of Wang Juzhen
Wang Juzhen, a Chinese scientist, has a saying about the failure of the experiment, which is called "if we continue to work, there is still 50% hope of success, otherwise, there will be 100% failure."
2. Tolstoy's score
When talking about the evaluation of people, Tolstoy, a great Russian writer, compares people to a score. He said: "a person is like a score, his actual ability is like a numerator, and his evaluation of himself is like a denominator. The greater the denominator, the smaller the score."
1. The essence of mathematics lies in its freedom. Cantor
2. In the field of mathematics, the art of asking questions is more important than the art of solving them
3. No problem can touch people's feelings as deeply as infinity. Few other ideas can inspire reason to produce fruitful ideas as infinity. However, no other concept needs to be clarified as infinity
4. Mathematics is an infinite science. Hermann wail
5. Problems are the heart of mathematics
6. As long as a branch of science can raise a large number of questions, it is full of vitality, and the lack of questions indicates the termination or decline of independent development
7. Some beautiful theorems in mathematics have such characteristics: they are easy to be induced from facts, but the proof is very deep
3. Lebakov's constants and variables
Russian historian rebakov said in his use of time: "time is a constant, but it is a 'variable' for diligent people. People who use 'minutes' to calculate time spend 59 times more time than people who use' hours'
2、 Writing mottos with symbols
4. The minus sign of Hua Luogeng
Hua Luogeng, a famous mathematician in China, pointed out when talking about learning and exploration: "in learning, we should dare to do subtraction, that is, subtracting the parts that have been solved by our predecessors. We need to explore and solve those problems that have not been solved."
5. Edison's plus sign
Edison, the great inventor, used a plus sign to describe genius. He said: "genius = 1% inspiration + 99% perspiration."
6. The sign of Dimitrov
When commenting on the work of a day, Dimitrov, a famous international worker's movement activist, said: "we should make use of our time to think about what we have done in a day, whether it's a positive sign or a negative sign. If it's a plus sign, we will make progress. If it's a minus sign, we have to learn lessons and take measures."
3、 Aphorism written in formula
7. Einstein's formula
When talking about the secret of success, Einstein, the greatest scientist in modern times, wrote down a formula: a = x + y + Z. a stands for success, x stands for hard work, y stands for correct methods, and Z stands for less empty talk. "
"If you use the small circle to represent what you have learned and the big circle to represent what I have learned, then the area of the big circle is a little more, but the blank space outside the two circles is our ignorance. The bigger the circle is, the more ignorance the circle contacts." - Zeno
Cauchy, 1789 – 1857
Men pass away,but their deeds abide.
People always die, but their achievements last forever
Laplace (1749 – 1827)
What we know is not much.What we do not know is immense.
What we know is little, what we don't know is infinite
C. Hermite (1822 – 1901)
Abel has left mathematicians enough to keep them busy for 500 years.
When evaluating Abel, he once said, "what Abel left behind can keep mathematicians busy for 500 years."
Poisson (1781-1840)
"Life is good for only two things,discovering mathematics and teaching mathematics"
There are only two things in life: developing mathematics and teaching mathematics
Einstein (1879-1955)
I don't believe in mathematics.
I don't believe in mathematics
Imagination is more important than knowledge.
Imagination is more important than knowledge
Do not worry about your difficulties in mathematics,I assure you that mine are greater.
Don't worry about your math, I promise I'll have more
Science without religion is lame; religion without science is blind.
Without religion, science is not convincing. Without science, religion becomes blind
Gauss, Karl Friedrich, 1777-1855
God does arithmetic.
God will count
Few,but ripe.
Better less, but better

When four people cross the bridge at night, they only have one flashlight, one for 1 minute, one for 2 minutes, one for 5 minutes and one for 10 minutes. They can only cross the bridge twice at a time

It takes at least 10 + 1 + 2 + 1 + 5, 19 minutes in total

How to solve binary quadratic equation