@vijay_chandola said:Range of a..? I guess a could be anything.For example, roots of the equation k*(x-1)*(x-2)=0 lie in interval (0, 3).but coefficient of x^2 could be anything, as 'k' is an independent term.What are the options?
@Torque024 said:Please someone help!Find the range of aGiven that the roots of quadratic equation ax^2 + bx + c =0 lie in the interval (0,3).
@Torque024 said:So there is no method to find the exact range in this case?@ScareCrow28 options se ho jayega, but exact range niklegi kaise?
@chillfactor said:Yeah, 0 is correct.n² + 89n + 2010 = k²n² + 89n + 2010 - k² = 0For n to be integer, D should be perfect sq89² - 8040 + 4k² = a²(2k - a)(2k + a) = 119 = 1*119 = 7*17k = 30 and 6n² + 89n + 2010 = 30²n = -74, -15n² + 89n + 2010 = 6²n = -47, -42So, given expression can not be a perfect sq for any positive n.Find the natural number n such that product of all positive divisors of n is 2011^2016
@Torque024 said:If a, b, c, d are real numbers with a^2 + b^2 + c^2 + d^2 = 100, then what is the maximum value of 2a + 3b + 6c + 24d?
@Torque024 said:45If a, b, c, d are real numbers with a^2 + b^2 + c^2 + d^2 = 100, then what is the maximum value of 2a + 3b + 6c + 24d?
@sujamait said:Find all triples (a; b; c) of natural numbers such that lcm(a; b; c) = a + b + c.
@Torque024 said:If a, b, c, d are real numbers with a^2 + b^2 + c^2 + d^2 = 100, then what is the maximum value of 2a + 3b + 6c + 24d?
@Torque024 said:If a, b, c, d are real numbers with a^2 + b^2 + c^2 + d^2 = 100, then what is the maximum value of 2a + 3b + 6c + 24d?
@sujamait said:I dont have OAFind all pairs of positive integers (n; m) satisfying 3n^2 + 3n + 7 = m^3
@Cat.Aspirant123 said:A company has two kinds of employees supervisor and clerks. The total monthly salary of theemployees is Rs. 2,85,000. What is the total number of employees in that company?A. The ratio of the number of supervisor to that of clerk in the company is 4 : 5.B. The total monthly salary of all the supervisors is 28% more than that of all clerks.C. 20% of the clerk €™s monthly salary is Rs. 250.a) Only A and B togetherb) Only A and C togetherc) Only B and C togetherd) A, B and C togethere) Question can €™t be answered even after using all the information
@gnehagarg said:3n^2+3n+1+6=m^3Add n^3 to both sidesn^3+3n^2+3n+1+6=m^3+n^3(n+1)^3+6=m^3+n^3M^3+n^3 is of form 9k or 9k+1 or 9k-1(n+1)^3+6 is of form 9k+6 or 9k+5 or 9k+7no solution
Clerk's 20% salary is Rs. 250. So, actual salary will be Rs. 1250.
Let x be the total combined salry fo clerk's. Supervisor's total salary is 28% more than clerks. So, supervisors total salary will be 1.28x.
N0w, x+1.28x = 2,85,000.
x = 1,25,000.
Number of clerks = 1,25,000/1,250=100
Number of supervisor is = 4*100/5 =80.
Hope this helps. All three conditions used.
@chillfactor said:Find all positive integers n for which n ˛ + 89n + 2010 is a perfect square.
@MikelArteta said:How'd you get this - M^3+n^3 is of form 9k or 9k+1 or 9k-1Because if a number n^3 is of the form 9k,9k+1,9k-1 then m^3 + n^3 could be of the form9k,9k+1,9k+2,9k+7,9k+8
@Cat.Aspirant123 said:In a mixed collection of peacocks and deer, if legs are counted they are 40 but if heads arecounted, they are just 15. How many peacocks are there?