搜搜考试网求解一道SAT1的数学题?
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求解一道SAT1的数学题?
If x > 2^(1000),which of the following is greatest
(x + 2)^2 – 2
(x – 2)^2 + 2
(x/2) ^ 2
(2x)^2/2
(x^2+2)/2
答案这里不给.回复给我.有问题我继续追问.
If x > 2^(1000),which of the following is greatest
(x + 2)^2 – 2
(x – 2)^2 + 2
(x/2) ^ 2
(2x)^2/2
(x^2+2)/2
答案这里不给.回复给我.有问题我继续追问.
答案是(2x)^2/2
令A=(x + 2)^2 – 2=x^2+4x+2 B=(x- 2)^2 + 2=x^2-4x+6 C=(x/2) ^ 2=(x^2)/4
D=(2x)^2/2=2x^2 E=(x^2+2)/2=(x^2)/2+1
则A-B=8x-4>0,从而A>B .A-C=(3x^2)/4+4x+2>0,从而A>C.
A-E=(x^2)/2+4x+1>0,从而A>E
D-A=x^2-4x-2=x(x-4)-2>8×4-2>0 (因为x > 2^(1000)>2^3=8),从而D>A
D is greatest.
令A=(x + 2)^2 – 2=x^2+4x+2 B=(x- 2)^2 + 2=x^2-4x+6 C=(x/2) ^ 2=(x^2)/4
D=(2x)^2/2=2x^2 E=(x^2+2)/2=(x^2)/2+1
则A-B=8x-4>0,从而A>B .A-C=(3x^2)/4+4x+2>0,从而A>C.
A-E=(x^2)/2+4x+1>0,从而A>E
D-A=x^2-4x-2=x(x-4)-2>8×4-2>0 (因为x > 2^(1000)>2^3=8),从而D>A
D is greatest.