Mister Exam
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How to use it?
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Identical expressions
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Similar expressions
- (x2-y2–1)3–x2y3=0
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What you mean?
- -x^2*y^3 + (x^2 + y^2 - 1*1)^3 = 0
You entered:
(x2+y2–1)3–x2y3=0
What you mean?
(x2+y2–1)3–x2y3=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
(x2 + y2 - 1)*3 - x2*y3 = 0
$$- x_{2} y_{3} + \left(x_{2} + y_{2} - 1\right) 3 = 0$$
Detail solution
Given the linear equation:
Expand brackets in the left part
Looking for similar summands in the left part:
Move free summands (without y2)
from left part to right part, we given:
$$- x_{2} y_{3} + 3 x_{2} + 3 y_{2} = 3$$
Move the summands with the other variables
from left part to right part, we given:
$$- x_{2} y_{3} + 3 y_{2} = 3 - 3 x_{2}$$
Divide both parts of the equation by (3*y2 - x2*y3)/y2
We get the answer: y2 = 1 - x2 + x2*y3/3
(x2+y2-1)*3-x2*y3 = 0
Expand brackets in the left part
x2*3+y2*3-1*3-x2*y3 = 0
Looking for similar summands in the left part:
-3 + 3*x2 + 3*y2 - x2*y3 = 0
Move free summands (without y2)
from left part to right part, we given:
$$- x_{2} y_{3} + 3 x_{2} + 3 y_{2} = 3$$
Move the summands with the other variables
from left part to right part, we given:
$$- x_{2} y_{3} + 3 y_{2} = 3 - 3 x_{2}$$
Divide both parts of the equation by (3*y2 - x2*y3)/y2
y2 = 3 - 3*x2 / ((3*y2 - x2*y3)/y2)
We get the answer: y2 = 1 - x2 + x2*y3/3
The graph
Sum and product of roots
[src]
sum
x2*y3
0 + 1 - x2 + -----
3
$$\left(\frac{x_{2} y_{3}}{3} - x_{2} + 1\right) + 0$$
=
x2*y3
1 - x2 + -----
3
$$\frac{x_{2} y_{3}}{3} - x_{2} + 1$$
product
/ x2*y3\ 1*|1 - x2 + -----| \ 3 /
$$1 \left(\frac{x_{2} y_{3}}{3} - x_{2} + 1\right)$$
=
x2*y3
1 - x2 + -----
3
$$\frac{x_{2} y_{3}}{3} - x_{2} + 1$$
1 - x2 + x2*y3/3