若a,b,c,d为非0实数,且(a2+b2)d2-2b(a+c)d+b2+c2=0.求证:b/a=c/b=d(2是平方)别误解
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若a,b,c,d为非0实数,且(a2+b2)d2-2b(a+c)d+b2+c2=0.求证:b/a=c/b=d(2是平方)别误解
若a,b,c,d为非0实数,且(a2+b2)d2-2b(a+c)d+b2+c2=0.求证:b/a=c/b=d
(2是平方)别误解
若a,b,c,d为非0实数,且(a2+b2)d2-2b(a+c)d+b2+c2=0.求证:b/a=c/b=d(2是平方)别误解
(a^2+b^2)*d^2-2b(a+c)d+b^2+c^2=0
=> a^2*d^2+b^2*d^2-2abd-2bcd+b^2+c^2=0
=> (a^2*d^2-2abd+b^2)+(b^2*d^2-2bcd+c^2)=0
=> (ad-b)^2+(bd-c)^2=0
=> ad-b=0 and bd-c=0 (因为只有每一项都等于0,他们的平方才能等0)
=> ad=b and bd=c
=> 因为a、b、c、d为非零实数,所以a,b可以做分母
b/a=d and c/b=d
=> b/a=c/b=d