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19 votes
X³=729 solve the equation

User Aufheben
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1 Answer

11 votes
11 votes

Answer:

x = 9

Explanation:

Rearrange


\sf \rightarrow x^3 - 729 = 0

Factor using (a-b) × (a^2 +ab +b^2)

a^3 + a^2b + ab^2 - ba^2 - b^2a - b^3 =

a^3 + (a^2b-ba^2) + (ab^2-b^2a) - b^3 =

a^3 + 0 + 0 - b^3 =

a^3 - b^3

x^3 = x^1

Rearrange(Using polynomial/cube roots)

(x - 9) × (x2 + 9x + 81) = 0

Subtract/Add

x - 9 = 0 = 9

x^2 + 9x = -81

-81 + 81/4

-243/4

x^2 + 9x + (81/4) = -243/4

(x + (9/2)) × (x + (9/2)) = (x + (9/2)) × 2

(x + (9/2))2 = -243/4

x^2 + 9x + 81 = 0

√243 = 3 × 3 × 3 × 3 × 3 = 3 × 3 × √3 = ±9 × √3

= ±9x = (-9 ± 9 × 1.732(i)) / 2

= ±9x

Divide by 9 (Absolute value: positive)

|9/9| = x

Reverse, re-arranging x (Assuming x = 1)

x = |9/x|

Thus,

x = 9

Hope this helped, let me know if anything confuses you, and I will try my best to address that. Have a good day!

User Mike Ramsey
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