Question

已知x＝根号3＋根号2,y＝根号3－根号2,求代数式3x^2-5xy+3y^2的值.

Answer 1

3x^2-5xy+3y^2=3x^2-6xy+3y^2+xy=3(x^2-2xy+y^2)+xy.

=3(x-y)^2)+xy=3[√3+√2-(√3-√2)]^2+(√3+√2)(√3-√2).

=3(2√2)^2+[(√3)^2-(√2)^2].

=3*8+(3-2).

∴原式=25.