Question
I. x2 + 91 = 20x II. 10y2 -
29y + 21 = 0 In the following question two equations are given in variables x and y. You have to solve these equations and determine the relation between x and y.Solution
I. x2 + 91 = 20x => x2 - 20x + 91 = 0 => x2 - 13x - 7x + 91 = 0 =>x(x - 13) - 7(x - 13) = 0 => (x - 13) (x - 7) = 0 => x = 13, 7 II. 10y2 - 29y + 21 = 0 => 10y2 - 14y - 15y + 21 = 0 => 2y(5y - 7) - 3(5y - 7) = 0 => (5y - 7) (2y - 3) = 0 => y = 7/5, 3/2 Hence, x > y. Alternate Method: if signs of quadratic equation is - ve and +ve respectively then the roots of equation will be +ve and +ve. So, roots of first equation = x = 13, 7 So, roots of second equation = y = 7/5, 3/2 After comparing we can conclude that x > y.
17    18      14       ?      7       32
...7 7 28 252 ?
...94Â Â Â 115Â Â Â 138Â Â Â 163Â Â Â Â 190Â Â Â Â ?
62, 87, 137, ?, 312, 437
135, 148, ?, 184, 207, 236
8    13    36    123    ?   2585
195% of 1420 + 72 × 25 =?
70, 69, 73, 64,80, 55, ?
64, 66, 69, 74, 81, ?
What value should come in the place of (?) in the following number series?
14, 43, 132, 401, 1210, ?, 10928
