Mate de Vita
Kelli

2008 Oct 4 • 2453
159 ₧

2 (unrelated) inequalities I have to solve:

sqrt(1-x) - sqrt(x) > 3/sqrt(5)

and

sqrt(12-(12/x^2)) - sqrt(x^2-(12/x^2)) < x^2

I can't figure out what to do with the square roots. I tried multiplying the first with (sqrt(1-x) + sqrt(x)) but that just moves the square roots to the other side. How do I begin solving an inequality like this?

Down Rodeo
Cap'n Moth of the Firehouse


2007 Oct 19 • 5486
57,583 ₧

OK, so, my first question is what are these for? If they're for a homework question or such I am slightly confused as Wolfram Alpha says there are no solutions to the first one. I'm inclined to agree. Certainly there's no way to make it much nicer.

Second one: Wolfie. It's a bit complicated. 4th roots of 3? No thanks.

Rockbomb
Dog fucker (but in a good way now)

2009 Nov 14 • 2045

I have no idea what's going on, but I'm gonna just agree with DR in attempt to make myself appear intelligent. I hope you're right, DR... my reputation depends on it.

SRAW
Rocket Man

2007 Nov 6 • 2525
601 ₧

err can't you just solve the first one by using a calculator on the right side and factorizing on the left then send just the square over?

SRAW
Rocket Man

2007 Nov 6 • 2525
601 ₧

and also on the left side, doesnt sqrt(1-x) = sqrt(1) - sqrt(x), in which case it should be easier but I'm probably wrong

Mate de Vita
Kelli

2008 Oct 4 • 2453
159 ₧

Yeah, the first one is a bit weird, since the roots of x and 1-x would imply that x is between 0 and 1 (otherwise the roots wouldn't be real numbers), which would mean those two square roots would also be between 0 and 1. I don't see how you could subtract two numbers like that to get something greater than 3/sqrt(5) (which is greater than 1).

This was kind of homework, it was a preparation for a test. Hopefully I don't get something like this in the actual test

Down Rodeo
Cap'n Moth of the Firehouse


2007 Oct 19 • 5486
57,583 ₧

Just ask the teacher. As far as I can tell there is no solution to the first one. Moreover I can see no situation where you'd have to manipulate something like this, be it in further education or a job or in day-to-day life.