Question

if x=2^2/3 - 2^1/3 -2. then prove that x^3+6x^2+18x+18=0

Answer 1

Hi ,

x = 2^2/3 - 2^1/3 - 2 ( given )

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

( x + 2 )³ = ( 2^2/3 - 2^1/3 )³

x³+6x²+12x+ 8=2-2-3×2^2/32^1/3( 2^2/3-2^1/3)

x³+6x²+12x+8 = -3×2× ( x + 2 ) [ from ( 1 ) ]

x³ + 6x² + 12x + 8 = -( 6x + 12 )

x³ + 6x² + 12x + 6x + 8 + 12 = 0

x³ + 6x² + 18x + 18 = 0

Hence proved.

I hope this helps you.

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