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< async src="//pagead2.googlesyndication.com/pagead/js/adsbygoogle.js"> If the equations x^2+ax+b=0 and x^2+px+q=0 have a common root, prove that(a-p)(bp-aq)=(b-q)^2 Solve the following equations for 0<=x<=360 tan2x+tanx=1-tan2xtanx

最佳解答:

let the common root be m m^2+am+b=0 .....(1) m^2+pm+q=0 .....(2) (1)-(2), we have am-pm=-(b-q) m=-(b-q)/(a-p)....... (3) put (3) into (1) [-(b-q)/(a-p)]^2-a(b-q)/(a-p)+b=0 (b-q)^2-(b-q)(a-p)a+b(a-p)^2=0 (b-q)^2=(a-p)[a(b-q)-b(a-p)] =(a-p)(bp-aq) tan2x+tanx=1-tan2xtanx (tan2x+tanx)/(1-tan2xtanx )=1 .. using tan(A+B)=(tanA+tanB)/(1-tanAtanB) tan3x=1 3x=45 , 225, 405, 585, 765, 945 x=15, 75, 135, 195, 255, 315

其他解答:4E350C6F8B48ECA2