Question

a,b为实数ac=b2(平方),a+b+c=3求b的范围

Answer 1

ac=b^2

a+c=3-b

(a+c)^2=(3-b)^2 (1)

2ac=2b^2 (2)

(1)-(2)

a^2+c^2=-b^2-6b+9>=0 (3)

因此有

3*2^0.5-3>=b>=-3*2^0.5-3