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Algebra

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Tutorials, How to solve quickly Concept articles, Question sets, Solution sets and Videos on Algebra. Mainly for SSC CGL competitive test.

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How to factorize 25 selected quadratic equations quickly by factor analysis

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In school exams or in competitive exams, how quickly and accurately you can factorize a quadratic equation is always a problem we have to grapple with. In this session a comprehensive method to factorize quadratic equations of various difficulties is presented through an exercise of 25 selected problems followed by explanatory solutions...

Algebraic proof of Least value of sum of reciprocals for any number of positive variables

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The result of the least value of sum of reciprocals, used in Algebra represents an important principle of value sharing.

For two positive real variables $a$ and $b$ for example, if $a+b=1$, the least value of sum of reciprocals of $a$ and $b$ will occur when the value of the sum 1 is shared equally between the two variables. This remarkable equal value sharing principle hold true for any number of variables as well as for any positive sum of the variables...

SSC CGL Tier II level Solution Set 14 Algebra 5 video Part 2

This is the second part of the fifth solution set of SSC CGL Tier II algebra. A few of this set of 5 problems are tricky and need application of advanced pattern discovery and concepts and methods for quick solution. Important concepts and techniques used are, pattern discovery, suitable substitution, principle of zero sum of square expressions, denominator simplification, missing element pattern...

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SSC CGL Tier II level Solution Set 14 Algebra 5 video Part 1

This is the first part of the fifth solution set of SSC CGL Tier II algebra. A number of this set of 5 problems are difficult and posed challenges for quick solution. Important concepts and techniques used are, pattern discovery, conversion to sum of inverses, surd elimination in sum of inverses, surd elimination condition, abstraction...

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SSC CGL Tier II level Solution Set 9 Algebra 4 video Part 2

This is the second part of the fourth solution set of SSC CGL Tier II algebra. A few of this set of 5 problems need application of advanced pattern discovery and concepts and methods for quick solution. Important concepts and techniques used are, pattern discovery, principle of zero sum of square terms, componendo technique, extra element pattern, roots of a quadratic equation, dummy variable substitution, sum of inverses conversion, abstraction, compact form of cube of sum, denominator simplification, and mathematical reasoning...

Embedded thumbnail for SSC CGL Tier II level Solution Set 9 Algebra 4 video Part 2

SSC CGL Tier II level Solution Set 9 Algebra 4 video Part 1

This is the first part of the fourth solution set of SSC CGL Tier II algebra. A few of this set of 5 problems are tricky and posed a bit of a challenge for quick solution. Important concepts and techniques used are, pattern discovery, maximum simplification of target, algebraic ratios, HCF reintroduction technique, target expression extraction, sum of inverses conversion, and mathematical reasoning...

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SSC CGL Tier II level Solution Set 3 Algebra 3 video Part 2

This is the second part of the third solution set of SSC CGL Tier II algebra. A few of this set of 5 problems need application of advanced pattern discovery and concepts and methods for quick solution. Important concepts and techniques used are, pattern discovery, indices, equalization of power, base equalization technique, missing element pattern, similarity increase technique, numerator equalization, coefficient comparison, variable elimination by substitution, solving a simpler problem and mathematical reasoning...

Embedded thumbnail for SSC CGL Tier II level Solution Set 3 Algebra 3 video Part 2

SSC CGL Tier II level Solution Set 3 Algebra 3 video Part 1

This is the first part of the third solution set of SSC CGL Tier II algebra. A few of this set of 5 problems are tricky and posed a bit of a challenge for quick solution. Important concepts and techniques used are, pattern discovery, abstraction, dummy variable substitution, minima of sum of inverses, balanced expression in power of two variables, modified two-factor sum of inverses, inequality analysis, substitution of ratio of two variables, principle of zero sum of square terms, square root concept, and mathematical reasoning...

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