Equations and Inequalities with Rationals

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spear33

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Jan 30, 2006
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22
Question 1
(3t^2 + 52t)^(1/4) = 4

I raised all of this to a power of 4 and got
3t^2 + 52t = 256

Then if I set it up for a quadratic thing its
3t^2 + 52t -256 = 0

Does this seem right so far?


Question 2

[sqrt r+5] - 2 = [sqrt r-1]

I squared each side and got
4 - 4*[sqrt r + 5] + r + 5 = r - 1

I know I have to square each side again, but I'm not sure what it comes out to.
 
spear33 said:
Then if I set it up for a quadratic thing its
3t^2 + 52t -256 = 0

Does this seem right so far?
Click to expand...

Yes, it does.

spear33 said:
4 - 4*[sqrt r + 5] + r + 5 = r - 1

I know I have to square each side again, but I'm not sure what it comes out to.
Click to expand...

You will know what it comes out to if you square both sides.

:lol:

Isolate the radical on one side of the equals sign, and collect like terms on the other side before squaring.

WARNING! Remember, whenever you square both sides of an equation to solve it, you MUST check all of your solutions to be sure that they satisfy the original equation because the act of squaring can sometimes introduce false solutions.

Let us know if you still need help with these problems. Please post your work, and explain why you're stuck.

~ Mark
 
For the first one If I plug it into the quadratic equation I get

-52 +- [sqrt 52^2 - 4 * 3 * -256] / (2*3)

Which reduces to
-52 +- 8306688 / 6

Which reduces to
-52 +- 138448

So am I wrong or is this equation just unsolvable or something like that?

I'll start working on the other one again.
 
spear33 said:
For the first one If I plug it into the quadratic equation I get

-52 +- [sqrt 52^2 - 4 * 3 * -256] / (2*3)

Which reduces to
-52 +- 8306688 / 6
Somehow this number is not correct. Refigure.
Which reduces to
-52 +- 138448

So am I wrong or is this equation just unsolvable or something like that?

I'll start working on the other one again.
Click to expand...
 
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