Question

已知a,b,c都是实数,且(a^2+b^2)x^2-2b(a+b)x+b^2+c^2=0,试证明c/b=b/a=x

Answer 1

(a^2+b^2)x^2-2b(a+c)x+b^2+c^2=0

(a^2x^2-2abx+b^2)+(b^2x^2-2bcx+c^2)=0

(ax-b)^2+(bx-c)^2=0

ax-b=0,bx-c=0

x=b/a,x=c/b

所以

c/b=b/a=x