Question

已知x=2－根号3分之一,y=2＋根号3分之一,求5x^2＋xy＋5y^2的值

Answer 1

x=1/(2-√3)

=(2+√3)/[(2+√3)(2-√3)]

=(2+√3)/(2²-√3²)

=(2+√3)/(4-3)

=2+√3

y=1/(2+√3)

=(2-√3)/[(2-√3)(2+√3)]

=(2-√3)/(2²-√3²)

=(2-√3)/(4-3)

=2-√3

5x²+xy+5y²

=5(2+√3)²+(2+√3)(2-√3)+5(2-√3)²

=5(4+4√3+3)+4-3+5(4-4√3+3)

=35+20√3+4-3+35-20√3

=71