Help with maths

Mate de Vita
Kelli

2008 Oct 4 • 2414
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? ...and that's the bottom line because Mate de Vita said so.

Who controls the past, controls the future. Who controls the present, controls the past.

Down Rodeo
Cap'n Moth of the Firehouse


2007 Oct 19 • 5327
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. Everyone stares when you walk in the room, they stare when you go....

Rockbomb
Dog fucker

2009 Nov 13 • 1942
-190 ₧

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 • 2146
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 • 2146
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 • 2414
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 ...and that's the bottom line because Mate de Vita said so.

Who controls the past, controls the future. Who controls the present, controls the past.

Down Rodeo
Cap'n Moth of the Firehouse


2007 Oct 19 • 5327
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. Everyone stares when you walk in the room, they stare when you go....