试从x=by+cz,y=cz+ax,z=ax+by,消去x,y,z.求a,b,c间的关系式.
方程12x³-28x²+17x-3=0之根为a,b,c,已知b=a+1,求a,b,c.
证明: cos(α+β-γ)+cos(α-β+γ)-cos(β+γ-α)-cos(α+β+γ)=4cosα∙sinβ∙sinγ.
设人眼在墙顶上观察一塔,测得塔之全长所夹之角为θ,设墙高为h尺,墙与塔之距离为d尺.试证:(h²+d²)sinθ/(hsinθ+dcosθ)尺为塔这高.
试判别方程x²+2xy-8y²+2x+14y-3=0之图形的性质.
一圆经过两点(2,-3),(-4,-1),而其中心在直线3y+x-18=0上,求圆的方程.
试证arcsinx+arcsiny=arcsin(x+y).
设α,β,γ为三角形内角,求证tg(α/2)∙tg(β/2)+tg(β/2)∙tg(γ/2)+tg(γ/2)∙tg(α/2)=1.
析a2b+ab2-a2c+ac2-2abc-b2c+bc2之因式.
Factor the following expressions: a(b + c)² + b(c + a)² + c(a + b)² - 4abc
Factor the following expressions:x(y - z)³ + y(z -x)³ + z(x - y)³
Resolve (1+52x+30x2-24x3)/(3x2-x-1)2 into partial fractions.
Factor the following:4a-16b+4a+1.
Factor the following:4(a-b)²-12(a-b)(e+9e²)