help me out this root problems

**question:1. ³√[3(³√x-1/³√x)]=2, then ³√[x]+1/³√[x]= what....**

question 2 If a=2b and b =4c, then ³√[a²/16bc](Bow)

question 3 the sides of a triangle are denoted by x,y,z. Area of the triangle and semi-perimeter of the triangle are denoted by P and q respectively. If P =√[q(q-x)(q-y)(q-z) and x+y-z = y+z-x = z+x-y = 4. Find P [in square units]

question 4. If a is any natural number, then a³-1/a³ will always be greater than or equal to

option 1. 3{a+1/a} option 2. a+1/a option 3. [a³+1/a³] option 4. 3(a+1/a)

**i am only 8th... so please explain clearly.. i already posted the question.. i didn't get the answer and so i again posted.. this time help me out..please..**

thanks a lot...(Bow)

Re: help me out this root problems

Hi Kohila,

Here are some thoughts on **Question 2**: If a=2b and b =4c, then ³√[a²/16bc].

*It requires to determine the value of ³√[a²/16bc]. Since the exact values of a, b, c are not provided, we need to know the relationships among a, b, c and make appropriate substitutions to factorize ³√[a²/16bc].

*The provided constraints, i.e., a=2b and b=4c, are just what we want to know---the relationships among a, b, c.

*From a=2b and b=4c we observe that both a and c relate to b. So we could substitute a and c in ³√[a²/16bc] with b. More specifically, we have a=2b and c=b/4.

*Now transform ³√[a²/16bc] to ³√[(2b)²/16b(b/4)] and I'm sure you could proceed with the rest:)

Re: help me out this root problems

Hi Kohila,

Here are some thoughts on **Question 3**. Hope they are helpful.

*the key point to solve p is to determine the values of q, q-x, q-y, q-z.

*semi-perimeter q=(x+y+z)/2, then we have:

q-x=(y+z-x)/2 where (y+z-x)'s value is assigned. So we can determine the value of q-x and that of q-y, q-z similarly.

*Now only the value of q=(x+y+z)/2 is left to determine. Please observe the provided constraints as follows:

x + y - z =4

-x + y + z =4

x - y +z =4

Any clue? All three variables x, y, and z happen three times in three provided equations: two times of + and one time of -. Combine all them then we get exactly (x+y+z) and therefore the value of q.

Now you could try find the values of q, q-x, q-y, q-z accordingly~

Re: help me out this root problems

Re: help me out this root problems

wow, it's really a neat solution!

Re: help me out this root problems