- #1
mathdad
- 1,283
- 1
Suppose that the circle x^2 + 2Ax + y^2 + 2By = C has two intercepts, a and b, and two y-intercepts, c and d.
Prove that a•b - c•d = 0.
How is this started?
Prove that a•b - c•d = 0.
How is this started?
RTCNTC said:In the last example, the sum of the roots turned to be s = -b/a. Can the product p be -ba?
That's why I provided a link. In my opinion, this information is useful, at least to verify the answers, i.e., formulas for sum and product of roots of a quadratic polynomial.RTCNTC said:I know nothing about Vieta.
No, using the formula $(x+y)(x-y)=x^2-y^2$ we getRTCNTC said:Here is the product P:
P = (4a^2b^2 + 4ac - b^2)/(4a^2)
I am not sure what you mean (LaTeX formulas are also typed). If my post is displayed incorrectly, the best thing would be to post a screenshot to illustrate the problem.RTCNTC said:Your typed letters are blocking your Latex work.
Evgeny.Makarov said:I am not sure what you mean (LaTeX formulas are also typed). If my post is displayed incorrectly, the best thing would be to post a screenshot to illustrate the problem.
greg1313 said:Inline latex throws RTCNTC's cell phone off (he does not use a desktop).
In regards to the problem,
Label the positive x-intercept a, the negative x-intercept b, the positive y-intercept c and the negative y-intercept d. These four points around the origin are the vertices of a cyclic orthodiagonal quadrilateral, so angle bdc is equivalent to angle bac and angle acd is equivalent to angle abd. Using the tangent ratio, b/d = c/a which implies ab = cd, ab - cd = 0; QED.
Proving a statement means providing evidence or logical reasoning to support the truth or validity of the statement.
To prove a given statement, you can use mathematical or scientific principles, experiments, observations, or logical arguments to demonstrate the truth or validity of the statement.
The purpose of proving a statement is to provide evidence or logical reasoning to support the truth or validity of the statement, and to convince others of its accuracy.
No, proving a statement and proving a hypothesis are not the same. Proving a statement involves demonstrating the truth or validity of a specific statement, while proving a hypothesis involves testing and confirming a proposed explanation for a phenomenon.
It is generally accepted in science that no statement can be proven 100% true, as new evidence or discoveries may arise in the future that can challenge or change our understanding of the statement. However, a statement can be supported by overwhelming evidence and widely accepted by the scientific community.