If a = b and b > 0 and a > 0, then 1 = 2 a>0 and b>0 a = b ab = b^{2}ab - a^{2}= b^{2}- a^{2}a(b-a) = (b+a)(b-a) a = (b+a) a = a + a (substituting a for b) a = 2a a/a = 2a/a 1 = 2 a = x [true for some a's and x's] a+a = a+x [add a to both sides] 2a = a+x [a+a = 2a] 2a-2x = a+x-2x [subtract 2x from both sides] 2(a-x) = a+x-2x [2a-2x = 2(a-x)] 2(a-x) = a-x [x-2x = -x] 2 = 1 [divide both sides by a-x] a = b a^{2}= ab a^{2}- b^{2}= ab - b^{2}(a + b)(a - b) = b(a - b) a + b = b 2b = b 2 = 1 (x + 1)^{2}= x^{2}+ 2x + 1 (x + 1)^{2}- (2x + 1) = x^{2}(x + 1)^{2}- (2x + 1) - x(2x + 1) = x^{2}- x(2x + 1) (x + 1)^{2}- (x + 1)(2x + 1) + (1/4)(2x + 1)^{2}= x^{2}- x(2x + 1) + (1/4)(2x + 1)^{2}[(x + 1) - (1/2)(2x + 1)]^{2}= [x - (1/2)(2x + 1)]^{2}(x + 1) - (1/2)(2x + 1) = x - (1/2)(2x + 1) x + 1 = x 1 = 0

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Fun With Math-General Stuff Main Page Units and Prefixes Really Big Number Names Numeric Terms Glossary Proposed New Digits For Base 12, 16, 20 Systems Base Names Formulas: Geometry Number Series Perfect Numbers-definition Perfect Numbers Hexadecimal Math Table 0-10 + 0-10 and 0-10 x 0-10 Hex Decimal Integer Conversion Table How To Compute The Square Root Roman Numerals Binary Math Table Roman Numeral Math Tables What's 13 times 7? Prove That 1 = 2 Number Tricks It's Impossible Pi In Your Face Wind Chill Factor Relative Heat Index Computerized Long Form Math Fractional Tables: Addition Fractional Tables: Multiplication

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Fun With Math Fun With Math-General Stuff Fun With Math-All About The Numbers Fun With Math-2-D Addition Tables Fun With Math-2-D Multiplication Tables Fun With Math-Division Tables with Remainders Fun With Math-Powers and Roots of 2 and 3 Fun With Math-n to the kth Power Fun With Math-Perfect Right Angles Fun With Math-Right Angle Addition Tables - 2D Fun With Math-Factorials Fun With Math-Triangulars Fun With Math-Least Common Multiples Fun With Math-Greatest Common Denominator Fun With Math-Prime Numbers Fun With Math-Factors of Each Number Fun With Math-Prime Factors of Each Number Fun With Math-Decimal to Hexadecimal Conversion Fun With Math-Hexadecimal Addition Tables Fun With Math-Hexadecimal Multiplication Tables

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