If \( x \, \text{¤} \, y = (x + y)^2 - (x - y)^2 \), then \( \sqrt{5} \, \text{¤} \, \sqrt{5} = \)

x ⋄ y = ( x + y ) 2 − ( x − y ) 2 = x 2 + 2 x y + y 2 − ( x 2 − 2 x y + y 2 ) = x 2 + 2 x y + y 2 − x 2 + 2 x y − y 2 = 4 x y 5 ​ ⋄ 5 ​ = 4 ⋅ 5 ​ ⋅ 5 ​ = 4 ⋅ 5 = 20

Answered by Anonymous | 2024-06-10

The calculation of 5 ​ ¤ 5 ​ using the defined operation results in 20. By applying the operation step-by-step, we found that ( 5 ​ + 5 ​ ) 2 equals 20 and ( 5 ​ − 5 ​ ) 2 equals 0. Therefore, the final answer is 20.
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Answered by Anonymous | 2024-12-23