Mathematics

Mathematics

Problem

Let m1,m2m_1, m_2 be the slopes of two adjacent sides of a square of side aa such that a2+11a+3(m12+m22)=220a^2 + 11a + 3(m_1^2 + m_2^2) = 220 . If one vertex of the square is (10(cos⁡α−sin⁡α),10(sin⁡α+cos⁡α))(10(\cos \alpha - \sin \alpha), 10(\sin \alpha + \cos \alpha)) , where α∈(0,π2)\alpha \in (0, \frac{\pi}{2}) and the equation of one diagonal is (cos⁡α−sin⁡α)x+(sin⁡α+cos⁡α)y=10(\cos \alpha - \sin \alpha)x + (\sin \alpha + \cos \alpha)y = 10 , then 72(sin⁡4α+cos⁡4α)+a2−3a+1372(\sin^4 \alpha + \cos^4 \alpha) + a^2 - 3a + 13 is equal to: [Main July 29, 2022 (II)] (a) 119 (b) 128 (c) 145 (d) 155

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