Question

a³+1/a³=18 then prove A= (3 + √5)/2​

Answer 1

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Explanation:

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Answer 2

Explanation:

উত্তর টা a = (3 +/- √5)/2 হবে।

(a + 1/a)^3 = a^3 + 1/a^3 + 3.a.1/a (a + 1/a).

বা, a^3 + 1/a^3 = (a + 1/a)^3 - 3 (a + 1/a) = 18.

Or, (a + 1/a)^3 - 3(a + 1/a) - 18 = 0

Or, y^3 - 3a - 18 = 0 [ let (a + 1/a) = y ]

Or, y^3 - 3y^2 + 3y^2 - 9y + 6y - 18 = 0.

Or, (y - 3)(y^2 + 3y + 6) = 0

Or, (y - 3) = 0 & (y^2 + 3y + 6) = 0

Put y = a + 1/a, we get a + 1/a - 3 = 0

Or, a^2 - 3a + 1 = 0

Or a = [- ( - 3) +/- √{( - 3)^2 - 4. 1. 1}]/2.1

Or, a = [ 3 +/- √5]/2