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Let a, b, c, and d be real numbers such that a > b and c > d. Enter the letters of the statements below that must be true.

 

(A) a + c > b + d

 

(B) 2a + 3c > 2b + 3d

 

(C) a - c > b - d

 

(D) ac > bd

 

(E) a^2 + c^2 > b^2 + d^2

 

(F) a^3 + c^3 > b^3 + d^3

 May 16, 2020
 #1
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Obviously the first is true, the second is also true.
The third is not because the difference between the a and c is not stated. ac is not neccesarily greater than bd because c could be negative and a could be positive but b and d could both be negative giving negative > positive which is obviously not true
The third is not true  because if the absolute value of b > absolute value a then b^2 > a^2 and for c and d as well.
a^3 + c^3  is true because absolute value doesnt matter here
To summarize A, B and F are true and the others are not

 May 16, 2020

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