perplexus.info :: Just Math : Irrational Decision

Irrational Decision (Posted on 2015-11-15)

Let A be an irrational number and let N is an integer > 1.

Is ^N√(A + √(A²-1)) + ^N√( A - √(A²-1)) always an irrational number?

Give reasons for your answer.

See The Solution Submitted by K Sengupta

Rating: 5.0000 (1 votes)

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

re(3): N=2 only

| Comment 4 of 6 |

(In reply to re(2): N=2 only by Jer)

well it is stated in the problem that A is irrational.

Assume x=sqrt(2A+2) is rational

then

x^2=2A+2

A=(x^2-2)/2

if x is rational then so is (x^2-2)/2 and thus so is A

which contradicts A being irrational, thus x must be irrational as well.

Posted by Daniel on 2015-11-16 20:53:52

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