If x is equal to 1 + root 2 then find the value of expression x power 4 - x cube - 2 x square - 3 x + 1
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x=1+ √2
Formula
(a+b)² = a² + b² +2ab
(a+b)³ = a³ + b³ + 3a²b + 3ab²
Let Y = x⁴ + x³ - 2x² - 3x +1
x⁴ = [(1+√2)²]²
= [ (1+2+2√2)]²
= [3+2√2]²
= [9+ 8+ 12√2]
= 17+12√2
x³ = (1+√2 )³
= (1 + 2√2 + 3√2 + 6)
= ( 7 + 5√2 )
2x² = 2( 1+√2)²
= 2(1+2+2√2)
= 2(3 + 2√2)
= 6 + 4√2
Y = (17 + 12√2) + ( 7 + 5√2 ) - (6 + 4√2)
- (3 +3√2) +1
= 16 +10√2
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