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Several math problems in senior one! ! !
The first question: substitution method

Option a, 3. F (ab) = (ab) 2 = f (a) × f (b) is satisfied.

Option b, 2.f(ab)=3(a+b)=f(a)+f(b)? satisfy

C option, temporarily skip

Option d, 2.f(ab)=ln(ab)=f(a)+f(b) is satisfied.

The elimination method chooses C. This question examines your familiarity with the formula.

Question 2: Find the side length a of the cube.

√3a=2R?

3√3? a^3=8R^3

a^3=(8√3? R^3)/9

Third question

1.AB is perpendicular to the CD at 90 degrees. Taking the midpoint e of CD, it is easy to prove that AE and BE are perpendicular to CD, and CD is the vertical plane AE and Be.

2. Further to the above question, the perpendicular line from A to BE passes through BE to O, A0 belongs to face AEB, so A0 is perpendicular to CD and A0 is perpendicular to be, so A0 is perpendicular to face BCD, so the angle ABO is the angle to be formed.

Let AB=2, BO=2/3BE=2√3? /3,cot? Answer? =√3? /3? Use inverse cotangent a=Arccot? √3? /3

Question four? Write your own

(1) simultaneously F (x) = x 2-2x-3 and g(x), and the conditions of roots are judged by finding the balance of roots.

(2) For a problem similar to 1, judge the situation of roots and get inequalities.