(x^1/3+x^-1/3)^2?

2 ⤊

2007-08-06 16:46:37 · 4 answers · asked by swtaznbj34 2 in Science & Mathematics ➔ Mathematics

4 answers

[ x^(1/3) + 1 / x^(1/3) ] ²
x^(2/3) + 2 + 1/ x^(2/3)

2007-08-07 04:05:26 · answer #1 · answered by Como 7 · 2⤊ 0⤋

(x^1/3 + x^-1/3)^2
= x^2/3 + 2(x^1/3 x^-1/3) + (x^-1/3)^2
-----> x^1/3(x^-1/3) = x^(1/3-1/3) = x^0 = 1
-----> (x^-1/3)^2 = x^2/3
= x^2/3 + 2(1) + x^2/3
= 2x^2/3 + 2 or 2(x^2/3 + 1)

2007-08-06 17:01:00 · answer #2 · answered by Enginurse 2 · 0⤊ 1⤋

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

2007-08-06 16:53:10 · answer #3 · answered by PaeKm 3 · 0⤊ 0⤋

(x^1/3+x^-1/3)(x^1/3+x^-1/3)
x^2/3+x^0+x^0+x^2/3
2x^2/3+2
2[x^(2/3) + 1]

2007-08-06 17:06:07 · answer #4 · answered by ferdie 2 · 0⤊ 1⤋