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Home » Premier segment : \( \frac30075 = 4 \) heures. - Sterling Industries

Premier segment : \( \frac30075 = 4 \) heures. - Sterling Industries

📅 April 16, 2026 👤 scraface

Apr 16, 2026

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📌 x^2 - (4y^2 - 4yz + z^2) = x^2 - 4y^2 + 4yz - z^2

📌 Thus, the simplified expansion is $ oxed{x^2 - 4y^2 + 4yz - z^2} $.

📌 Question: Factor the expression $ 9x^2 - 30xy + 25y^2 - 16z^2 $ completely.

📌 First, group the first three terms:

📌 Note that $ 9x^2 - 30xy + 25y^2 = (3x - 5y)^2 $, a perfect square.

📌 This is a difference of squares: $ a^2 - b^2 = (a - b)(a + b) $, with $ a = 3x - 5y $, $ b = 4z $.

📌 The fully factored form is $ oxed{(3x - 5y - 4z)(3x - 5y + 4z)} $.Question: Compute the sum of the roots of the equation $ u^{3/2} - 4u + 3\sqrt{u} = 0 $, given that all roots are non-negative real numbers.

📌 Solution: Let $ v = \sqrt{u} $, so $ u = v^2 $. Substituting into the equation gives $ v^3 - 4v^2 + 3v = 0 $. Factoring yields $ v(v^2 - 4v + 3) = 0 $, which simplifies to $ v(v-1)(v-3) = 0 $. Thus, $ v = 0, 1, 3 $, corresponding to $ u = 0, 1, 9 $. The sum of the roots is $ 0 + 1 + 9 = 10 $. oxed{10}

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