Question
If 27x3 - 8y3 = (3x - Ay) X
(Bx2 + 4y2 + Cxy), then find the value of 3 X (2A + 6B) - 2C.Solution
27x3 - 8y3 = (3x - Ay) X (Bx2 + 4y2 + Cxy) We know that, a3 - b3 = (a - b) X (a2 + b2 + ab) So, 27x3 - 8y3 = (3x)3 - (2y)3 = (3x - 2y) X (9x2 + 4y2 + 3x X 2y) = (3x - 2y) X (9x2 + 4y2 + 6xy) So, (3x - Ay) X (Bx2 + 4y2 + Cxy) = (3x - 2y) X (9x2 + 4y2 + 6xy) On comparing coefficients of LHS and RHS, we get, A = 2, B = 9, and C = 6 So, 3 X (2A + 6B) - 2C = 3 X {2 X 2 + 6 X 9} - 2 X 6 = 3 X (4 + 54) - 12 = 3 X 58 - 12 = 174 - 12 = 162
23, 27, 39, 59, ?, 123
What will come in place of the question mark (?) in the following series?
4, 2605, 5309, 8118, ?
In each of the following number series, one term is missing. Find the missing term.
2, 6, 18, 54, 162, ?
25   25   37.5   ?   328.125   1804.6875
32   48   96   ?   720   2520
What will come in place of (?) question mark in the given number series.
12, 27, 44, 65, ?, 139
What will come in place of the question mark (?) in the following series?
12, 13, 27, ?, 329, 1646
312, 302, 282, ?, 212, 162
23Â Â Â Â 44Â Â Â Â 64Â Â Â Â 83Â Â Â Â Â ? Â Â Â Â Â 118
...What will come in place of the question mark (?) in the following series?
18, 22, 34, 70, 178, ?
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