Question
If x4 + x2 y2 +
y4 = 37 and x2 – xy + y2 = 5, then what is the value of xy ?Solution
x4 + x2 y2 + y2 = 37 and x2 – xy + y2 = 5 --- (1) As we know, (x4 + x2 y2 + y2) = (x2 – xy + y2) (x2 + xy + y2) ⇒ x2 + xy + y2 = 37/5 ⇒ x2 – xy + y2 = 7.4 --- (2) Subtract equation (2) from equation (1) ⇒ 2xy = 2.4 ⇒ xy = 1.2
12 7 10 25 107 ?
...30, 39, 66, ? , 174, 255
 47                         54          ?             74          87          ...
65    69   77 93  ?    189
18 113 559 2247 6721 13451
...219 365 511 ? 803 949
...10Â Â Â Â Â Â Â Â 6Â Â Â Â Â Â Â Â Â Â Â Â Â Â 5Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 8.5Â Â Â Â Â Â Â Â Â Â 16Â Â Â Â Â Â Â Â Â Â Â Â Â ?
...22   39    58    81   ?      141
Complete the series.
19, 23, 26, 30, 33, ?
1240 600 ? 140 90 25
...
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