C1 - Prove that... Watch

lapsaJ
Badges: 2
Rep:
?
#1
Report Thread starter 13 years ago
#1
7b) Given that x and y are integers, prove that

1/(x - "y) + 1/(x + "y)

can be written in the form p/q where p and q are both intergers.

(" is the square root of)

Hope someone can help!!
0
reply
Libertine
Badges: 1
Rep:
?
#2
Report 13 years ago
#2
(Original post by lapsaj)
7b) Given that x and y are integers, prove that

1/(x - "y) + 1/(x + "y)

can be written in the form p/q where p and q are both intergers.
1/(x-√y) + 1/(x+√y) Put over common denominator of (x-√y)(x+√y)
= (x+√y)/[(x-√y)(x+√y)] + (x-√y)/[(x-√y)(x+√y)]
But (x-√y)(x+√y) = x²-y

So insert that in to get:
(x+√y+x-√y)/(x²-y)
= 2x/(x²-y)

Since x and y are integers, it can be written as p/q
0
reply
Chewwy
Badges: 15
Rep:
?
#3
Report 13 years ago
#3
1/(x - √y) + 1/(x + √y) = (x+√y + x - √y)/(x+√y)(x-√y) = 2x/(x^2 - y)

both numerator and rational, given x,y integers. so it's rational.
0
reply
//Mike
Badges: 0
Rep:
?
#4
Report 13 years ago
#4
If you simplify the expression:

[1 / (x - √y)] + [1 / (x + √y)]
= [(x + √y) + (x - √y)] / (x + √y)(x - √y)
= 2x / (x² - y)

Since x and y are both integers, 2x will be an integer value, and x² - y will also be an integer value.
0
reply
lapsaJ
Badges: 2
Rep:
?
#5
Report Thread starter 13 years ago
#5
Thanks a lot guys, amazed at the really quick response!!
0
reply
X

Quick Reply

Attached files
Write a reply...
Reply
new posts
Latest
My Feed

See more of what you like on
The Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

Personalise

University open days

  • University of East Anglia
    All Departments Open 13:00-17:00. Find out more about our diverse range of subject areas and career progression in the Arts & Humanities, Social Sciences, Medicine & Health Sciences, and the Sciences. Postgraduate
    Wed, 30 Jan '19
  • Aston University
    Postgraduate Open Day Postgraduate
    Wed, 30 Jan '19
  • Solent University
    Careers in maritime Undergraduate
    Sat, 2 Feb '19

Brexit: Given the chance now, would you vote leave or remain?

Remain (1130)
79.02%
Leave (300)
20.98%

Watched Threads

View All