CPhill

Here's a graph of this one.........

The solutions (roots) are: x = 0 (as Alan noted) and x ≈ .354336....Notice how the lead term "over-powers" the graph very quickly as x moves away from zero in a positive direction. Also, as x gets more and more negative, the first two terms → 0 and the graph has a limit of 1 on the left hand side.....

I believe the second one is this....

5(3x+1)^¼=10     divide both sides by 5

(3x+1)^¼= 2       raise each side to the 4th power

3x + 1  = 16       subtract 1 from both sides

3x = 15              divide both sides by 3

x = 5

When someone requests to borrow my ruler....I always suspect that something's "a foot"

......or so......

Sorry, Nataszaa, but I believe my answer to the second one was correct......we could "simplify" it further as:

4x + (4/3)x√(6)    (I actually prefer it as a single fraction, but it's arbitrary)

(I believe Aziz forgot to distribute the x over the second term)

(2√7)/(√3-√5)

The trick here is just to multiply by the conjugate of the denominator in both the numerator and denominator....so we have.....

[(2√7)/(√3-√5)] *[(√3+√5) / (√3+√5)] =

[2√(21) + 2√(35)] / (3-5) =

[(2)[√(21) + √(35)]] / (-2)  =

-[√(21) + √(35)]

--------------------------------------------------------------------------------------------------

The next one is similar........

(4x)/(3-√6) * [ (3+√6) / (3+√6)] =

[(4x)(3+√6)]/[9 -6] =

[12x + 4x√6] / [3]

14sqrt20-3sqrt125.....so we have...

14√(4*5) - 3√(25*5) =

14(2)√5 - 3(5)√5 =

28√5 - 15√5 =

13√5

----------------------------------------------------------------------------------------------------

cubedroot 54+cubedroot 16 =

³√54 + ³√16 =

³√(27*2) + ³√(8*2)  =

(3)³√(2) + (2)³√(2)  =

(5) ³√(2)

Here's an easy way to compare two fractions (without having to get a common denominator!!)

3/8   3/4

Multipy the denominator of the second fraction by the numerator of the first fraction and put the result (12) over the first fraction. Then multiply the denominator of the first fraction times the numerator of the second fraction and put the result (24) over the second fraction..so we have...

12      24

3/8    3/4

Compare the results....the larger number is over the greater fraction...

Thus, 3/4 > 3/8  !!!

14√x+3√y

This one can't be simplified any more, Nataszaa. We can't add unlike radicals.

There is no answer to this. The right side always = -1 (x cannot = 0) and that will never equal the left side (.309).

Don't worry, Alan.....the questioner is not liable to forget how to find the LCM with two explanations......!!!