perplexus.info :: Numbers : sum, reciprocals, squares

Home > Numbers

sum, reciprocals, squares (Posted on 2022-03-22)

The sum of two numbers is 1.

The sum of the reciprocals of the numbers is 1.

Find the sum of the squares of the numbers (without finding the numbers themselves.)

What do you notice?

No Solution Yet Submitted by Jer

Rating: 4.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)

Solution

| Comment 3 of 4 |

Given 1/a + 1/b = 1

Multiply both sides by a we get

1 + a/b = a

=> 1 = a - a/b = a + b

=> b = -a/b

=> b^2 = -a

Similarly if we'd multiplied both sides by b we'd get

a^2 = -b

So a^2 + b^2 = -(a + b) = -1

Posted by tomarken on 2022-03-22 09:36:54

Please log in:

Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (0)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:


perplexus dot info