Given that the x power of 10 is 20 and the Y power of 10 is 1 / 5, then the x power of 9 / 3 is 2Y=

Given that the x power of 10 is 20 and the Y power of 10 is 1 / 5, then the x power of 9 / 3 is 2Y=

10^x=20
10^y=1/5
10^x/10^y=10^(x-y)=20/(1/5)=100=10^2
So X-Y = 2
9^x/3^2y=9^x/9^y=9^(x-y)=9^2=81

Y = (AX-1) / [(AX ^ 2 + 4ax + 3)] to the third power, the domain of definition belongs to R, and the value range of a is obtained
Process. Thank you!

If the domain belongs to R, the denominator is always not equal to 0
So the cubic root of (AX ^ 2 + 4ax + 3) is not equal to 0
That is, ax ^ 2 + 4ax + 3 is not equal to 0
If a = 0, then ax ^ 2 + 4ax + 3 = 3
If a is not equal to 0
Is a quadratic function
If it is not equal to 0, there is no intersection with X axis
So the discriminant is less than 0
So 16A ^ 2-12a

If FX = ax cubic + x increases monotonically in the interval [- 1,1], then the value range of a

F (x) = ax ^ 3 + x increases monotonically on [- 1,1],
Then f '(x) = 3ax ^ 2 + 1 = 0 has no real root on (- 1,1),
X = 0 obviously does not satisfy 3ax ^ 2 + 1 = 0,
From a = - 1 / (3x ^ 2) and x ^ 2 > = 1, a > = - 1 / 3 is obtained