Question

已知m(m-3)-(m^2-3n)=9,则(m^2+n^2)/2-mn的值为_______

如果a是方程x^2-5x+1=0的解，则代数式a^2+1/a^2的值为_____
若多项式x^2+px-18可化成两个一次二项式的积，则p的值为______

Answer 1

已知m(m-3)-(m^2-3n)=9,则(m^2+n^2)/2-mn的值为:9/2
m^2-3m-m^2+3n=9
-3m+3n=9
m-n=-3

(m^2+n^2)/2-mn
=(m^2+n^2-2mn)/2
=(m-n)^2/2
=(-3)^2/2
=9/2

如果a是方程x^2-5x+1=0的解，则代数式a^2+1/a^2的值为:23
a是方程x^2-5x+1=0的解
则a^2-5a+1=0
a-5+1/a=0
a+1/a=5

a^2+1/a^2
=(a+1/a)^2-2
=5^2-2
=25-2
=23

若多项式x^2+px-18可化成两个一次二项式的积，则p的值为:±17,±7,±3,0
x^2-17x-18=(x-18)(x+1)
x^2+17x-18=(x+18)(x-1)
x^2-7x-18=(x-9)(x+2)
x^2+7x-18=(x+9)(x-2)
x^2-3x-18=(x-6)(x+3)
x^2+3x-18=(x+6)(x-3)
x^2-18=(x+3√2)(x-3√2)