TADM2E 1.2 - Revision history

Aroonalok at 18:47, 17 May 2016

2016-05-17T18:47:41Z

2016-05-17T18:24:26Z

2014-09-11T18:22:29Z

Recovering wiki

2014-09-11T18:13:12Z

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<math>a = -2</math> 
<math>b = 3</math> 
<math>min(a,b) = -2</math> 
<math>a * b = (-2) * 3 = -6</math> 

-- Solution by Rajiv Seelam

← Older revision		Revision as of 18:47, 17 May 2016
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	In this case, if both the numbers lie between 0 and 1 then <math> ab<min(a,b) </math>		In this case, if both the numbers lie between 0 and 1 then <math> ab<min(a,b) </math>
		+
		+	--[[User:Aroonalok\|Aroonalok]] ([[User talk:Aroonalok\|talk]]) 14:47, 17 May 2016 (EDT)

← Older revision		Revision as of 18:24, 17 May 2016
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−	~~<math>a = -2</math><br>~~	+	Due to the symmetric nature of the problem (swapping ''a'' and ''b'' does not change the problem), let
−	~~<math>b = 3</math><br><br>~~
−	~~<math>min~~(a,b) ~~= -2</math><br>~~
−	~~<math>a * b = (-2) * 3 = -6</math><br><br><br>~~

−	-- ~~Solution by Rajiv Seelam~~	+	<math>min(a,b) = a</math>
		+
		+	We now have to show that there exist some real numbers for which the following holds true:
		+
		+	<math> ab<a </math>
		+	<math>\implies a(b-1)<0 </math>
		+
		+	So, the product of two numbers (''a'' and ''b-1'') is negative. This means one of the numbers is negative and the other is positive.
		+
		+	''Case I'' :
		+	<math>a < 0 \and b-1>0</math>
		+	<math>\implies a<0 \and b>1</math>
		+
		+	In this case, if one of the numbers is negative and the other is greater than 1 then <math> ab<min(a,b) </math>
		+
		+	''Case II'' :
		+	<math>a > 0 \and b-1<0</math>
		+	<math>\implies a>0 \and b<1</math>
		+	Since, <math> min(a,b) = a </math>
		+	<math>\implies a<b</math>
		+	<math>\implies 0<a<b<1 </math>
		+
		+	In this case, if both the numbers lie between 0 and 1 then <math> ab<min(a,b) </math>

@@ Line 1: / Line 1: @@
-&lt;math&gt;a = -2&lt;/math&gt;&lt;br&gt;
+<math>a = -2</math><br>
-&lt;math&gt;b = 3&lt;/math&gt;&lt;br&gt;&lt;br&gt;
+<math>b = 3</math><br><br>
-&lt;math&gt;min(a,b) = -2&lt;/math&gt;&lt;br&gt;
+<math>min(a,b) = -2</math><br>
-&lt;math&gt;a * b = (-2) * 3 = -6&lt;/math&gt;&lt;br&gt;&lt;br&gt;&lt;br&gt;
+<math>a * b = (-2) * 3 = -6</math><br><br><br>
 -- Solution by Rajiv Seelam