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Home » Thus, the dosage parameter is $ oxed{rac135} $. - Sterling Industries

Thus, the dosage parameter is $ oxed{rac135} $. - Sterling Industries

📅 April 16, 2026 👤 scraface

Apr 16, 2026

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📌 lpha^4 + 3 = alpha + b

📌 First compute \( lpha^2 \):

📌 lpha = 1 + i \Rightarrow lpha^2 = (1+i)^2 = 1 + 2i + i^2 = 1 + 2i - 1 = 2i

📌 lpha^4 = (lpha^2)^2 = (2i)^2 = 4i^2 = -4

📌 lpha^4 + 3 = -4 + 3 = -1 = a(1+i) + b = a + ai + b

📌 Equating real and imaginary parts:

📌 Real: \( a + b = -1 \)

📌 Imaginary: \( a = 0 \)

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Recognize this as a difference of squares:
16x^4 - 81y^4 = (4x^2)^2 - (9y^2)^2 = (4x^2 - 9y^2)(4x^2 + 9y^2)
Now notice that $ 4x^2 - 9y^2 $ is also a difference of squares:
4x^2 - 9y^2 = (2x - 3y)(2x + 3y)
So the full factorization is:
Final answer: $ \boxed{(2x - 3y)(2x + 3y)(4x^2 + 9y^2)} $
Question: Compute the square of $ 3\sqrt{2} - 2\sqrt{3} $.
Use the identity $ (a - b)^2 = a^2 - 2ab + b^2 $:
Compute each term:
2(3\sqrt{2})(2\sqrt{3}) = 12\sqrt{6}

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