If A > 0, show that A + (1/A) >= 2 .
K klreed2 New member Joined Jun 24, 2005 Messages 9 Jun 28, 2005 #1 If A > 0, show that A + (1/A) >= 2 .
S soroban Elite Member Joined Jan 28, 2005 Messages 5,586 Jun 28, 2005 #2 Hello, klreed2! If A > 0, show that A + (1/A) <u>></u> 2 Click to expand... For a positive number A: . (A - 1)<sup>2</sup> .<u>></u> .0 . . . . . Then we have: . A<sup>2</sup> - 2A + 1 .<u>></u> .0 . . . . . .which arranges to: . A<sup>2</sup> + 1 .<u>></u> .2A . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . . . . . . . . . . . . Divide by A: . A + -- .<u>></u> .2 . . . . . . . . . . . . . . . . . . . . . . . . . . A
Hello, klreed2! If A > 0, show that A + (1/A) <u>></u> 2 Click to expand... For a positive number A: . (A - 1)<sup>2</sup> .<u>></u> .0 . . . . . Then we have: . A<sup>2</sup> - 2A + 1 .<u>></u> .0 . . . . . .which arranges to: . A<sup>2</sup> + 1 .<u>></u> .2A . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . . . . . . . . . . . . Divide by A: . A + -- .<u>></u> .2 . . . . . . . . . . . . . . . . . . . . . . . . . . A