Question
If (x 4 + x 2 y 2 +
y 4 ) = 216 and (x 2 - xy + y 2 ) = 12, then find the value of '3xy'.Solution
x 2 - xy + y 2 = 12 -------- (I)
Using, (x 4 + x 2 y 2 + y 4 ) = (x 2 - xy + y 2 ) (x 2 + xy + y 2 )
216 = 12 X (x 2 + xy + y 2 )
Or, x 2 + xy + y 2 = 18 -------- (II)
On subtracting equation (II) from (I) ,
We get, x 2 - xy + y 2 - (x 2 + xy + y 2 ) = 12 - 18
Or, x 2 - xy + y 2 - x 2 - xy - y 2 = - 6
Or, 2xy = 6
Or, xy = 3
Required value = 3 X 3 = 9
5 12 26 47 ? 110
...80, 116, 52, ?, 8, 204
63, 74, ?, 129, 173, 228
48, 95, 283, 1129, ?, 33841
What will come in the place of questions (?) mark in the following questions.
160, 223, 271, 306, 330, ?
What will come in place of the question mark (?) in the following series?
77, 198, 342, 511, 707, ?
- What will come in place of (?) in the given number series.
121, 100, 81, 64, ?, 36 Find the missing number in the given number series.
5, 9, 18, 34, 59, ?1236, 1445, 1675, 1933, 2226, ?
124, 128, ?, 135, 110, 146
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