Question and Answers Forum
AllQuestion and Answers: Page 142
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Question and Answers Forum |
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AllQuestion and Answers: Page 142 |
| Find: 1−(sin30°)^2 + (sin30°)^4 − (sin30°)^6 + ... |
| If 2x = a + (√((4b^3 − a^3 )/(3a))) and 2y = a − (√((4b^3 − a^3 )/(3a))) then show that x^3 + y^3 = b^3 . |
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| Let a,b,c ∈R^+ , a+b+c=3 prove the following inequality (((2a−3)^2 )/b)+(((2b−3)^2 )/c)+(((2c−3)^2 )/a)≥((a^2 +b^2 )/(a+b))+((b^2 +c^2 )/(b+c))+((c^2 +a^2 )/(c+a)) |
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| If n ≥ 2 and U_n = (3 + (√5))^n + (3 − (√5))^n then prove that U_(n + 1) = 6U_n − 4U_(n − 1) . |
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| Find: (((1/2) + 1 + (3/2) + ... + 16)/((1/4) + (2/4) + (3/4) + ... + 8)) |
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| If x : y : z = a : b : c then show that (((a + b + c)/(x + y + z)))^3 = ((abc)/(xyz)) . |
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| Show that ((a^3 + b^3 )/(a^2 + b^2 )) > ((a^2 + b^2 )/(a + b)) |
| Find the 2023rd term in the sequence 2,3,5,6,7,8,10,11,12,13,14,15,17,18,... obtained by subtracting integer squares from natural numbers. |
| If a_1 = 1 and a_1 ∙ a_2 ∙ ... ∙ a_n = n^2 Find: a_2 + a_(13) = ? |
| If ((3cosx + 2sinx)/(cosx − sinx)) = 4 find ctgx = ? |
| Parvin leaves home to go to school. After walking 3/8 of the way, he remembers that he forgot his book. He goes back home, picks up his book, and arrives at school at the time he was originally supposed to. How many times did Parvin increase his initial speed to reach school on time ? |
| x ∈ R Find: max((5/(x^2 − 6x + 11))) = ? |
| If a^2 + a = 5 Find ((a^(−b) + a^(1−b) + a^(2−b) )/a^(−b) ) = ? |
| Find: log_2 (log_3 (log_4 64)) = ? |
| psinθcon^2 θ=a pcosθsin^2 θ=b p≠0 θ∈(0 ,(π/2)) prove p=(((a^2 +b^2 )^(3/2) )/(ab)) |
| If ((3a − b)/(x + y)) = ((3b − c)/(y + z)) = ((3c − a)/(z + x)) then show that ((a + b + c)/(x + y + z)) = ((a^(2 ) + b^2 + c^2 )/(ax + by + cz)) . |
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