Lemma

Algebra · Chapter 3 of 20

Inequalities

53 curated · 760 from open sources

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53
#TitleDifficultySourceTags
6The mean of twoEasyLemmaAM–GMSquares are nonnegative
766Smallest integer solutionEasyLemmaInequalities
767x plus its reciprocalEasyLemmaInequalities
768Squares below nineEasyLemmaInequalities
1644Positive inequality productEasyHall & KnightInequalitiesAM-GM inequality
1645Symmetric triple sum productEasyHall & KnightInequalitiesAM-GM inequality
1646Quantity and reciprocal sumEasyHall & KnightInequalitiesReciprocals
1647Cauchy-Schwarz case for two variablesEasyHall & KnightInequalitiesCauchy-Schwarz
1648Cauchy-Schwarz case for three variablesEasyHall & KnightInequalitiesCauchy-Schwarz
1652Symmetric InequalityEasyHall & KnightInequalitiesRearrangement Inequality
1657Cube of Sum InequalityEasyHall & KnightAM-GM inequalityInequalities
1672Logarithm boundsEasyHall & KnightInequalitiesLogarithms
1872Minimum sum of reciprocalsEasyHall & KnightInequalitiesAM-GM inequality
1649Exponential and logarithmic inequalitiesMediumHall & KnightInequalitiesLogarithms+1
1650Algebraic Inequality ProductMediumHall & KnightInequalitiesAM-GM inequality
1651Comparing Two ExpressionsMediumHall & KnightInequalitiesComparison
1653Sum of Products InequalityMediumHall & KnightInequalitiesAM-GM inequality
1654Squares InequalityMediumHall & KnightInequalitiesSum of Squares
1655Inequality with CubicsMediumHall & KnightInequalitiesFactoring
1656Range for an InequalityMediumHall & KnightInequalitiesCubic polynomials
1658Power and Odd Product InequalityMediumHall & KnightInequalitiesAM-GM inequality
1661Maximum value of a product of powersMediumHall & KnightMaximum and minimumAM-GM inequality
1662Minimum value of a rational expressionMediumHall & KnightMaximum and minimumAlgebraic manipulation
1663Fourth Power InequalityMediumHall & KnightInequalitiesPower Means
1664Sum of Cubes InequalityMediumHall & KnightInequalitiesMathematical Induction+1
1668Weighted Power InequalityMediumHall & KnightInequalitiesWeighted Means+1
1669Logarithmic inequality for powersMediumHall & KnightInequalitiesLogarithms+1
1670Fractional power inequalityMediumHall & KnightInequalitiesSequences & series
1671Harmonic progression power inequalityMediumHall & KnightInequalitiesHarmonic progression
1673Cauchy-Schwarz Inequality ApplicationMediumHall & KnightInequalitiesCauchy-Schwarz
1674Positivity of Symmetric ExpressionsMediumHall & KnightPolynomialsSymmetric polynomials+1
1675Power Inequality for ExponentsMediumHall & KnightExponentsInequalities+1
1676Weighted Arithmetic Mean InequalityMediumHall & KnightLogarithmsAM-GM inequality+1
1677Factorial Product InequalityMediumHall & KnightFactorialsAM-GM inequality+1
1866Factorial and Power InequalityMediumHall & KnightInequalitiesFactorials
1867Product and Power InequalityMediumHall & KnightInequalitiesArithmetic-Geometric Mean Inequality
1868Cubic variables inequality first partMediumHall & KnightInequalitiesAM-GM inequality
1869Cubic variables inequality second partMediumHall & KnightInequalities
1870Maximum of a polynomial productMediumHall & KnightInequalitiesMaxima and minima
1871Maximum of a fractional power productMediumHall & KnightInequalitiesMaxima and minima
1873Product inequality from sum constraintMediumHall & KnightInequalitiesAM-GM inequality
47Three fractions, at least threeDeepLemmaAM–GMProducts telescoping
50A dot product can't be too bigDeepLemmaCauchy–SchwarzSquares are nonnegative
971Inequality for four continued proportionalsDeepHall & Knightproportioninequality
1659Inequality with powers and rootsDeepHall & KnightInequalitiesMathematical Induction
1660Factorial inequalityDeepHall & KnightInequalitiesFactorials+1
1665Sum of Even PowersDeepHall & KnightInequalitiesHölder's Inequality+1
1666Growth of Exponential ExpressionsDeepHall & KnightInequalitiesCalculus+1
1667Descending Variables InequalityDeepHall & KnightInequalitiesLogarithmic Convexity
1678Minimum product of factorialsDeepHall & Knightfactorialinequalities+1
1874Triangle Side Quadratic Non-negativityDeepHall & KnightTrianglesQuadratic forms+1
1875Triangle Side Expression Sign ConstraintDeepHall & KnightTrianglesQuadratic forms+1
1899An inequality with positive numbersDeepHall & KnightLogarithmic inequalitiesAM-GM inequality

From open sources

760

Complete problems only, with worked solutions first. Show everything

#TitleDifficulty
21068which of the following inequalities indicates the set of all values of…Medium
21436Arun Kumar, Chennakesavan , Raghu and Krishnan always have discussions on various…Medium
23365Which of the following inequalities is equivalent to 10 + 2x >…Medium
239431/2, 1/4, 1/8, 1/16, 1/32,1/64, 1/128 Medium
26207which of the following inequalities indicates the set of all values of…Medium
26287What range of values of 'x' will satisfy the inequality 15x -…Medium
26505A manufacturer of a certain type of screw rejects any screw whose…Medium
26800Which of the following inequalities has a solution set, when graphed on…Medium
27856A manufacturer of a certain type of screw rejects any screw whose…Medium
28789a, b, c, d are positive integers such that exactly one of…Medium
28829Which of the following values of A satisfies the inequalityMedium
29683A right triangle ABC has to be constructed in the xy-plane so…Medium
32344What values of 'x' will be the solution to the inequality 15x…Medium
32676Right triangle RST can be constructed in the xy-plane such that RS…Medium
33017Which of the following inequalities is equivalent to –2 < x <…Medium
36587Solve the given two equations and find the inequality of X and…Medium
37956A right triangle ABC has to be constructed in the xy-plane so…Medium
38435A manufacturer of a certain type of screw rejects any screw whose…Medium
38560What inequality represents the condition 1<x<11Medium
39483For what range of values of 'x' will the inequality 15x -…Medium
39941A right triangle AEC has to be constructed in the xy-plane so…Medium
43823Right triangle ABC is to be drawn in the xy-plane so that…Medium
44163Solve the given two equations and find the inequality of X and…Medium
45182If "x" is an integer, which of the following inequalities have a…Medium
47373Krishnakumar, Raghunandan, Chinnan and Aibak had an interesting discussion on the following…Medium
479241/2, 1/4, 1/8, 1/16, Medium
487641/2, 1/4, Medium
49394which of the following inequalities indicates the set of all values of…Medium
52235Which value of x does statisfy the inequality 2x2 + x –…Medium
52386Which of the following is equivalent to the pair of inequalities x…Medium
55233Right triangle PQR is to be constructed in the xy-plane so that…Medium
55910A right triangle AWC has to be constructed in the xy-plane so…Medium
56215Which of the following values of x will satisfy the inequality x2…Medium
60708Which of the following inequalities has (have) a finite range of values…Medium
61157What is the smallest integer a > 0 such that the inequality…Medium
61896Which of the following inequalities is equivalent to 40 + 6x >…Medium
65156Which of the following inequalities is always true for any real number…Medium
65986How many solutions are possible for the inequality | x - 1…Medium
668771/2, 1/4, 1/8, 1/16, 1/32, Medium
68435If y = x +2, Find the range of real values of…Medium
69275How many distinct integer values of n satisfy the inequality||n-3| + 4|…Medium
70054A right triangle AQC has to be constructed in the xy-plane so…Medium
73777which of the following inequalities indicates the set of all values of…Medium
75090A right triangle ATC has to be constructed in the xy-plane so…Medium
75476Right triangle PQR is to be constructed in the xy-plane so that…Medium
76082Which of the following inequalities is represented by the following number lineMedium
76616Which of the following inequalities is equivalent to -24 > -4 -…Medium
786631/2, 1/4, 1/8 Medium
79590Which values of ‘x’ satisfies the inequality x2 - 3x + 2…Medium
79795Which of the following values of x do not satisfy the inequality…Medium
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