lg2与lg5的等差中项是（）.若x,y,z成等比数列,则（z-x）∧2+4（x-y）（y-x）=

Question

lg2与lg5的等差中项是（ ）.若x,y,z成等比数列,则（z-x）∧2+4（x-y）（y-x）=

Answer 1

lg2与lg5的等差中项是 :(lg2+lg5)/2=lg(2×5)/2=1/2
若x,y,z成等差数列,则2y=x+z
∴(z-x)²+4(x-y)(y-x)
=(z-x)²-4(x-y)²
=(z-x+2x-2y)(z-x-2x+2y)
=(x+z-2y)(z+2y-3x)
=0
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