Answered

If x and y are real numbers such that x > 1 and y < −1,

then which of the following inequalities must be true?

Ax/y> 1
B|s|^2 > |y|
Cx/3− 5 > y/3 − 5
Dx^2 + 1 > y^2 + 1
Ex^(−2) > y^(−2)

Verified Answer :

\(x > 1\ \wedge\ y < -1\\\\A.\ \frac{x}{y} > 1-FALSE;example:x=2;\ y=-2\ then\\L=\frac{2}{-2}=-1;R=1;\ L < R\\\\B.\ |x|^2 > |y|-FALSE;example:x=2;\ y=-6\ then\\L=|2|^2=2^2=4;R=|-6|=6;\ L < R\\\\C.\ \frac{x}{3}-5 > \frac{y}{3}-5-TRUE;\frac{x}{3}-5 > \frac{y}{3}-5\to\frac{x}{3} > \frac{y}{3}\to x > y\)

\(D.\ x^2+1 > y^2+1-FALSE;example:x=2;\ y=-3\ then\\L=2^2+1=4+1=5;R=(-3)^2+1=9+1=10;L < R\\\\E.\ x^{-2} > y^{-2}-FALSE;example:x=3;\ y=-2\ then\\L=3^{-2}=\frac{1}{9};R=(-2)^{-2}=\frac{1}{4};\ L < R\)

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