×

# Some Number Problems

IF it is given that a+b=c+d AND ab=cd, does it imply that a=c and b=d or a=d and b=c?

Note by Keshav Gupta
4 years, 1 month ago

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold
- bulleted- list
• bulleted
• list
1. numbered2. list
1. numbered
2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)example link
> This is a quote
This is a quote
    # I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears as
Remember to wrap math in $$...$$ or $...$ to ensure proper formatting.
2 \times 3 $$2 \times 3$$
2^{34} $$2^{34}$$
a_{i-1} $$a_{i-1}$$
\frac{2}{3} $$\frac{2}{3}$$
\sqrt{2} $$\sqrt{2}$$
\sum_{i=1}^3 $$\sum_{i=1}^3$$
\sin \theta $$\sin \theta$$
\boxed{123} $$\boxed{123}$$

Sort by:

Squaring the 1st expression and subtracting the 2nd from the 1st and rearranging leads to the result: (a+c)(a-c) = (d+b)(d-b) But we already know that a-c = d-b, so we have (a+c) = (d+b), or a = d. Similarly for a = c, etc.

- 4 years, 1 month ago

Thankyou very much Sir! I researched about it and found other ways to prove it as well.. One would be to assume they are the roots of a polynomial, they should be equal because they would be the roots of the same polynomial. Thanks for you time again! :)

- 4 years, 1 month ago