x=1/(1+√2),求√(x^3+2x^2-x+8)

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x=1/(1+√2),求√(x^3+2x^2-x+8)

x=1/(1+√2),求√(x^3+2x^2-x+8)
x=1/(1+√2),求√(x^3+2x^2-x+8)

x=1/(1+√2),求√(x^3+2x^2-x+8)
x=1/(1+√2),
=√2-1
√(x^3+2x^2-x+8)
=√x(x+1)²-2x+8
=√2(√2-1)-2(√2-1)+8
=√8
=2√2

x=1/(1+√2),
=√2-1
√(x^3+2x^2-x+8)
=√x(x+1)²-2x+8
=√2(√2-1)-2(√2-1)+8
=√8
=2√2

x=1/(1+√2)=√2-1 => x+1=√2 => (x+1)^2=2 => x^2+2x+1=2 => x^2+2x=1
=>√(x^3+2x^2-x+8) =√[x(x^2+2x)-x+8] =√[x-x+8]= √8 =2√2

x=(1-√2)/(1+√2)(1-√2)
=(1-√2)/(1-2)
=√2-1
x+1=√2
√(x^3+2x^2-x+8)
=√x(x+1)²-2x+8
=√[2(√2-1)-2(√2-1)+8]
=√8
=2√2

2√2