Given a + B + C = 0, AB + BC + AC = 0, prove a = b = C = 0

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• 1. Prove that a ^ 2 + B ^ 2 + C ^ 2-ab-ac-bc is a nonnegative number
• 2. If we know the square of a + the square of B + the square of C - AB BC AC = 0, we can judge the size relation of ABC quickly
• 3. In △ ABC, ∠ ABC = 90 degrees, D, E on AB, ad = AC, be = BC, try to judge whether the size of ∠ DCE is related to the size of ∠ B, if so, ask for the relationship between them, determine the degree, and explain the reason wait anxiously A |\E | D C -----------B Can't upload graphics, so that means. I hope I can understand it. A. B and C are △ and there are lines from e to C and D to C respectively.
• 4. Given a & # 178; + B & # 178; + C & # 178; = AB + AC + BC, judge the relationship between a, B and C
• 5. Given that the lengths of three sides of a triangle a, B, C satisfy a & # 178; + B & # 178; + C & # 178; - AB BC AC = 0, try to judge the shape of the triangle
• 6. If the square of a + the square of B + the square of C - AB BC AC = 0, try to explore the size relationship between ABC
• 7. It is known that a, B and C are the three sides of the triangle ABC. The comparison of the square of (a + B + C) is 2 (AB + BC + AC)
• 8. The square of ab-b-bc + AC Factorization
• 9. A ^ 2 + B ^ 2 + C ^ 2-ab-bc-ac = 0, the size relationship of ABC ABC is all positive
• 10. Compare the size of a * + b * + C * and ab + BC + AC. * = 2
• 11. It is known that a + B + C = 2,0
• 12. In the triangle ABC, BC = a, AB + AC = L, make a vertical line from the bisector of the outer angle a 'of the angles B and C, and prove that BD * AE = fixed value with the perpendicular feet of D and E
• 13. Given △ ABC, linear L ⊥ AB, l ⊥ AC, prove L ⊥ BC
• 14. It is known that plane α and β satisfy α⊥ β, α∩ β = L, straight line AB is in plane α, ab ⊥ L, straight line BC and de are in plane β, and BC ⊥ de. the proof is AC ⊥ De
• 15. In △ ABC. Ab ⊥ AC, ad ⊥ BC in D, the proof: 1 / ad ^ 2 = 1 / AB ^ 2 + 1 / AC ^ 2 So in the tetrahedral ABCD, what kind of conjecture can you get by analogy with the above conclusion, and explain the reason
• 16. Given a + B + C = 0, prove AB + BC + AC = 1
• 17. There is a mathematical problem: a natural number a, a total of 10 divisors, including 1 and a, to find the product of these divisors
• 18. The natural number n has 45 positive divisors. The minimum value of n is______ ．
• 19. How many positive divisors does 75600 have? How many odd divisors? Point out the ideas, thank you!
• 20. The divisor of 120, All divisors of 120 (except 1) are written as the product of prime factors of 120