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Algebra Level 3

The value of the expression x 4 − 8 x 3 + 18 x 2 − 8 x + 2 x^4 - 8x^3 + 18x^2 - 8x + 2 when x = 2 + 3 x = 2 + \sqrt3 comes out to be K K . Then what is the value of K 3 K^3


The answer is 1.

Pankaj Joshi by Pankaj Joshi , 23, India

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3 solutions

Mhar Ariz Marino
Jan 14, 2015

again, it is better to be lucky than to be intelligent..

3 Helpful 0 Interesting 0 Brilliant 0 Confused
Jinay Patel
Mar 2, 2014

It is being given that x = 2 + 3^(1/2) x-2 = 3^(1/2) squaring two times it will given you the same expression but 1 less .

2 Helpful 0 Interesting 0 Brilliant 0 Confused

How are you so intelligent?

Jayakumar Krishnan - 6 years, 11 months ago

exp. = X^4 - 8X^3 + 16X^2 + 2X^2 - 8X + 8 - 6 ......FACTOR THE FIRST THREE AND LAST THREE
= X^2(X - 4)^2 + 2{ ( X - 2 )^2 -3 } =X^2(X - 4)^2 + 2{ ( X - 2 )^2 -3 } SUBSTITUTING THE VALUE OF X
={( 2 + V3 )( 2 + V3 - 4) }^2 + 2{ ( 2 + V3 - 2)^2 -3 } ={ -4 +3 }^2 + 2{ 0 }
K = 1


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