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Example (3):

If X = ?? v?? ?????? ?? = v?? - v??
v??-

Prove that: ?? ?????? ?? are conjugate numbers, then find the value of the
expression:

1) ??2 + 2 ?? ?? + ??2
2) ??2 + ?? ?? + ??2

Solution

X = ?? v?? x v?? + v?? = v?? + v??
v??- v?? + v??

Then X and Y are conjugate

1) ???? + ?? ?? ?? + ???? = ( ?? + ?? )?? = ( v?? + v?? + v?? - v?? )?? = 20

2) ???? + ?? ?? + ???? = ( ?? + ?? )?? - ???? = 20 - 2 = 18

1ST TERM MATH-PREP.2

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