AlgebraLast Updated : 27 Sep, 2023ReadDiscussCoursesAlgebraPlease wait while the activity loads.If this activity does not load, try refreshing your browser. Also, this page requires javascript. Please visit using a browser with javascript enabled.If loading fails, click here to try againQuestion 1Given two numbers x and y such that 1. x3 + y3 = 9 2. x + y = 3Find the value of x4+y4 2/371317Algebra Discuss itQuestion 1-Explanation: x3+y3 = (x + y) × (x2 − xy + y2) Putting given values of x3+y3 and (x + y) 9 = 3 × ((x+y)2 − 3xy) = 3 × (9 − 3xy) = 27 − 9xy 9xy = 18 xy = 2 x4 + y4 = (x2 + y2)2 - 2x2y2 = (x2 + y2)2 - 2*4 [Putting value of xy] = ((x + y)2 - 2xy)2 - 2*4 [Putting values of (x+y) and xy] = (9 - 4)2 - 2*4 = 17Question 2The value of x+1/2x is given as 2, then find the value of 8x3+1/x340/320/72840Algebra Discuss itQuestion 2-Explanation: x3 + 1/8x3 + 3.x.1/2x(x + 1/2x) = (x+1/2x)3x3 + 1/8x3 + 3 = 23x3 + 1/8x3 = 58x3 + 1/x3 = 5.8 = 40 Question 3If x takes only real numbers. For what value of x, the value of the expression: 4−6x−x2 will be maximum?-4-303Algebra Discuss itQuestion 3-Explanation: Differentiate and equate to 0 6+2x =0 x=−3Question 4For what value of x, the following equation: 5√x +12√x =13√x will be true?-203None of the aboveAlgebra Discuss itQuestion 4-Explanation: say x=117!=13for, x=2 and 3 also not possible x=4 52+122=132 169=169Question 5Solve for x in the equation: log(2x - 1) + log(3) = log(x + 5) x = -1/3 x = 1/3 x = 5/3 x = 8/5Algebra Discuss itQuestion 5-Explanation: Using the property of logarithms that states log(a) + log(b) = log(ab), we can simplify the equation as log(3(2x - 1)) = log(x + 5). Therefore, we have 6x - 3 = x + 5. Simplifying, we get 5x = 8, which gives us x = 8/5. Hence, the answer is D) x = 8/5.Question 6If the value of b2 + 1⁄b2 = 1, then find the value of b3 + 1⁄b3-1/12-2-4None of the aboveAlgebra Discuss itQuestion 6-Explanation: E = (b + 1⁄b)(b2 - 1 + 1⁄b2)Question 7 1 + 1/(x+4)x+41/x(x+4)/ xAlgebra Discuss itQuestion 7-Explanation: Question 8If a+b+c = 0, then the value of (a^2/bc) + (b^2/ac) + (c^2/ab) will be? 3210Algebra Discuss itQuestion 8-Explanation: Question 9Following instructions are to be used throughout the quiz:Each of the questions given below consists of a statement and/or a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statement(s) is/are sufficient to answer the given question.Read both the statements and Give answer(a) if the data in Statement I alone is sufficient to answer the question, while the data in Statement II alone is not sufficient to answer the question.(b) if the data in Statement II alone is sufficient to answer the question, while the data in Statement I alone is not sufficient to answer the question.(c) if the data in each Statement I and Statement II alone is sufficient to answer the question.(d) if the data even in both Statements I and II together are not sufficient to answer the question.(e) if the data in both Statements I and II together are necessary to answer the question.If x,y are integers, then (x2 + y2)1/2 is an integer?I) x2 + y2 is an integerII) x2 - 3y2 = 0ABCDEData Sufficiency Algebra Discuss itQuestion 9-Explanation: Statement 1: x2 + y2 is an integer Since x and y are integer x2+y2 can be any real number which may not be a perfect square so statement 1 alone cant prove whether (x2+y2)(½) is an integer or not. Statement 2: x2- 3y2 = 0 =>x2+y2-4y2=0 =>x2+y2=4y2 => (x2+y2)(½)= 2y Which is an integer because y is an integer.Question 104/15 of 5/7 of a number is greater than 4/9 of 2/5 of the same number by 8. What is half of that number?63063315105Algebra Discuss itQuestion 10-Explanation: Let the number be x. Then, 4/15 of 5x/7 = 4/9 of 2x/5 + 8 4/15 * 5x/7 = 4/9 * 2x/5 + 8 4x/21 = 8x/45 + 8 x/21 = 2x/45 + 2 x/21 = (2x + 90)/45 45x = 21(2x + 90) 45x = 42x + 90*21 3x = 90*21 x = 30*21 = 630. Half of the number will be x/2 x/2 = 630/2 = 315. 12 There are 20 questions to complete.You have completedquestionsquestionYour accuracy isCorrectWrongPartial-CreditYou have not finished your quiz. If you leave this page, your progress will be lost.Correct AnswerYou SelectedNot AttemptedFinal Score on QuizAttempted Questions CorrectAttempted Questions WrongQuestions Not AttemptedTotal Questions on QuizQuestion DetailsResultsDateScoreHintTime allowedminutessecondsTime usedAnswer Choice(s) SelectedQuestion Text Need more practice!Keep trying!Not bad!Good work!Perfect!