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Example (2):

If x = 4 ?????? ?? = 3-2v2 . write each of x and y such its denominator
2-v2 3+2v2

is a rational number, then find ?? + ??.

Solution:

X = ?? x ??+ v?? = 2 x ( ?? + v?? ) = 4 + 2v??
??-v?? ?? + v??

y= ??-??v?? x ??- ??v?? = 9 - 12v?? + 8 = 17 - 12v??
??+??v?? ??- ??v??

X + Y = 21 – 10 v??

Important remarks:

? ??2 + 2 ???? + ??2 = (?? + ??)2
? ??2 + ???? + ??2 = (?? + ??)2 - ????
? ??2 + ???? + ??2 = (?? + ??)2 - ????
? ??2 - 2???? + ??2 = (?? - ??)2
? ??2 - ???? + ??2 = (?? - ??)2 + ????
? ??2 + ??2 = (?? + ??)2 - 2????

1ST TERM MATH-PREP.2

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