Question

x=1+√2 find the value of expression x⁴-x³-2x²-3x+1​

Answer 1

Hope that it will b helpful

Answer 2

Answer:

2

Step-by-step explanation:

f(x) = x⁴-x³-2x²-3x+1​

divide both side by x²

f(x)/x² = x² - x - 2 - 3/x + 1/x²

          = x² + 1/x² - 2 - x - 1/x - 4/x

          = (x² + 1/x² - 2) - (x + 1/x) - 4/x

          = (x - 1/x)² - (x + 1/x) - 4/x ............(1)

∴ x = 1 + √2

1/x = √2 - 1

Therefore, x - 1/x = 2 [Put in (1)]

f(x)/x² = 2² - 2 - 4/x

          = 2 - 4/x

f(x)      = x² (2 - 4/x)

          = 2x² - 4x

[ ∴ x² = 3 + 2√2 ]

f(x)      = 2( 3 + 2√2) - 4(1 + √2)

          = 2 Ans.