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# A difficult Maths Question for you all to solve:- watch

1. 3√(x + a)^2 + 4* 3√(x - a)^2 = 5* 3√(x^2 - a^2)

x = ? (a is not equal to zero)

key: 3√ is "cube root"

Any solutions?
2. Factorises nicely into

{(x+a)-2(x-a)}^2/3 = (x^2-a^2)^1/3
(3a-x)^2 = x^2 - a^2
9a^2 - 6ax + x^2 = x^2 - a^2
10a^2 - 6ax = 0
2a(5a - 3x) = 0
x = 5a/3
3. (Original post by JamesF)
Factorises nicely into

{(x+a)-2(x-a)}^2/3 = (x^2-a^2)^1/3
(3a-x)^2 = x^2 - a^2
9a^2 - 6ax + x^2 = x^2 - a^2
10a^2 - 6ax = 0
2a(5a - 3x) = 0
x = 5a/3
I think ive done something wrong.
4. (Original post by JamesF)
I think ive done something wrong.
i was thinkin that aswell, but not sure what
5. Whooops, ive just realised ive done something amazingly stupid.
It doesnt factorise like that. It factorises into

((x+a)^1/3 - 2(x-a)^1/3)^2 = (x^2-a^2)^1/3

Unless ive done something else stupid...i think i should go to bed.
6. u=(x+a)^1/3
v=(x-a)^1/3
uv=(x²-a²)^1/3

u² + 4v² = 5uv
4v² - 5uv + u² = 0
(4v - u)(v - u) = 0
4v = u
v = u
===

4v = u
4(x - a)^1/3 = (x + a)^1/3
64(x - a) = (x + a)
63x = 65a
x = 65a/63
=======

v= u -> no solution
7. (Original post by Fermat)
u=(x+a)^1/3
v=(x-a)^1/3
uv=(x²-a²)^1/3

u² + 4v² = 5uv
4v² - 5uv + u² = 0
(4v - u)(v - u) = 0
4v = u
v = u
===

4v = u
4(x - a)^1/3 = (x + a)^1/3
64(x - a) = (x + a)
63x = 65a
x = 65a/63
=======

v= u -> no solution
i'm not even gonna ask what you done there!
8. (Original post by Fermat)
u=(x+a)^1/3
v=(x-a)^1/3
uv=(x²-a²)^1/3

u² + 4v² = 5uv
4v² - 5uv + u² = 0
(4v - u)(v - u) = 0
4v = u
v = u
===

4v = u
4(x - a)^1/3 = (x + a)^1/3
64(x - a) = (x + a)
63x = 65a
x = 65a/63
=======

v= u -> no solution
nice

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