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Question Number 54595 by ajfour last updated on 07/Feb/19
x+y=az+bx=cbz+xy=dFindyzintermsofa,b,c,d.
Commented by mr W last updated on 07/Feb/19
y=a−xz=c−bxb(c−bx)+x(a−x)=dx2+(b2−a)x+d−bc=0x=a−b2±(b2−a)2−4(d−bc)2yz=(a−x)(c−bx)⇒yz=[a+b2±(b2−a)2−4(d−bc)][2c+b3−ab±b(b2−a)2−4(d−bc)]4
Commented by ajfour last updated on 07/Feb/19
ThanksSir,butwecanmakeuseofeq.inx2onlytogetx2intermsofxandthensubstitute,doingthisigetyz=ac+b2c−bd−(c+b3)xigetyz=ac+b2c−bd−(c+b3)a−b2±(b2−a)2−4(d−bc)2.
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