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How to do high school mathematics, 24, 25?
25 First, substitute A into arithmetic progression, and there will be, x-a=a-y,

So a=(x+y)/2.

If you insert 20% into the geometric series, there is: x/b = b/c = c/y.

So xy = BCx≥b≥c≥y

(b+ 1)(c+ 1)=bc+c^2/y+b^2/x+ 1

(a+ 1)^2-(b+ 1)(c+ 1)=(x^2+y^2)/4+ 1+xy/2+x+y-bc-b-c- 1

= (x 2+y 2)/4-xy/2+x+y-b-c (xy=bc here)

=(x-y)^2/4+(x-b)+(y-c)

Because (x-y) 2 ≥ 0; (x-b)≥0; (y-c)≥0

Therefore, (a+1) 2-(b+1) (c+1) = (x-y) 2/4+(x-b)+(y-c) ≥ 0.

de:(A+ 1)2 ≥( B+ 1)(C+ 1)

24

Remember that F(x)=f(x+ 1/2),

To prove that F(x) is an even function, just prove that F(-x)=F(x),

That is, as long as it is proved that f(-x+)=f(x+ 1/2),

It is known that the images of functions f(x+ 1) and f(x) are symmetrical about y axis, and the images of functions f(x) and f(-x) are also symmetrical about y axis.

∴f(-x)=f(x+ 1).

So there is f (-x+)=f [-(x-)]

=f [(x-)+ 1]=f (x+ 1/2)

∴f(x+ 1/2) is an even function. /