Question
\( (5-2\sqrt {6)\times (5+2\sqrt {6)}} \)
Ask by Nichols Chandler. in Greece
Jan 21,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
Το γινόμενο \( (5 - 2\sqrt{6}) \times (5 + 2\sqrt{6}) \) ισούται με **1**.
Solution
Για να υπολογίσουμε το γινόμενο \( (5 - 2\sqrt{6}) \times (5 + 2\sqrt{6}) \), μπορούμε να χρησιμοποιήσουμε τον τύπο της διαφοράς των τετραγώνων:
\[
(a - b)(a + b) = a^2 - b^2
\]
Εφαρμόζοντας αυτόν τον τύπο:
\[
(5 - 2\sqrt{6})(5 + 2\sqrt{6}) = 5^2 - (2\sqrt{6})^2 = 25 - 4 \times 6 = 25 - 24 = 1
\]
Άρα, το αποτέλεσμα είναι **1**.
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Simplify this solution Bonus Knowledge
The expression \( (5-2\sqrt{6}) \times (5+2\sqrt{6}) \) is a classic example of using the difference of squares formula. When you multiply conjugates, you can simplify the expression as follows: \( a^2 - b^2 \), where \( a = 5 \) and \( b = 2\sqrt{6} \). Therefore, the result will be \( 5^2 - (2\sqrt{6})^2 = 25 - 24 = 1 \)! Another interesting tidbit is that this technique can be applied in various real-world situations, like simplifying complex expressions in physics or engineering equations. By recognizing the pattern of conjugates, we can quickly solve problems without laborious calculations, making life a bit easier!
