Question

二次根式的混合运算已知a=(√2)+1,求a的3次方-a的2次方-a+1

Answer 1

√2=a-1

(a-1)^2=2

a^2-2a+1=2

a^2-2a=1

a^2-2a+1=2

a^2+1=2a+2

a^3-a^2-a+1

=a^3-2a^2+a^2-a+1

=a(a^2-2a)+a^2-a+1

=a*1+a^2-a+1

=a^2+1

=2a+2

=2(√2+1)+2

=2√2+4