When the equation lg2x / LG (x + a) = 2, what is the value of a, the equation has a solution?

When the equation lg2x / LG (x + a) = 2, what is the value of a, the equation has a solution?

In order: lg2x = 2lg (x + a) 2x = (x + a) ^ 2: x ^ 2 + 2 (A-1) x + A ^ 2 = 0 and 2x ＞ 0, x + a ＞ 0, for the above univariate quadratic equation, △ = 4 [(A-1) ^ 2] - 4 (a ^ 2) = - 8A + 4, there are three cases: ① when △＞ 0, - 8A + 4 ＞ 0, a ＜ 1 / 2, the equation has two solutions, x = {2-2a ± [radical (4-8a)} / 2 = 1-A ± [root

When a is a value, the equation (lg2x) / LG (x + a) = 2 has one solution and two solutions,
How to start?

(lg2x) / LG (x + a) = 2, 2lg (x + a) = (lg2x), restriction condition: x > 0, (x + a) > 0, (x + a) is not equal to 1, that is, (x + a) ^ 2 = 2XX ^ 2 + 2 (A-1) x + A ^ 2 = 0, there is only one solution, or two solutions, or zero solutions, which should be discussed later

On the equation LG (a-5x) = LG (9-x ^ 2) - lgx of X, the value range of a when there is a solution

lg(a-5x)=lg(9-x^2)-lgx
a-5x>0
a>5x
x0
-3

56 * 23 = how much

1288

Given the image of quadratic function y = ax & sup2; + BX + C as shown in the figure, judge the sign of the following formula
1.a_____ 0,b_____ 0,c_____ zero
2.a+b+c_________ zero
3.a-b+c_________ zero
4.b²-4ac________ 0
The opening of the image is downward, and the intersection with the X axis is (- 1,0), (- 3,0), and the intersection with the Y axis is (0, - 1)

a

Addition and subtraction of rational numbers 2.4 + 0.5 + (- 3.2) - 2.4-4.7

Negative 7.4

Given sin (x + y) / cos (X-Y) = m / N, then TaNx / tany =?

If TaNx / tany is required, then x, y ≠ π / 2 + K π, and Y ≠ K π (k is an integer), then cosxcosy ≠ 0
sin(x+y)/cos(x-y)=m/n
(sinxcosy+cosxsiny)/(cosxcosy+sinxsiny)=m/n
(TaNx + tany) / (1 + tanxtany) = m / n

2. Fill in the box of the following equation and the operation symbol in the circle, so that the equal sign holds (the operation symbol in the two expressions cannot be the same): □0 □ = - 6; □0 □ = - 6

-2*3=-6
(-5)+(-1)=-6
Is that what this means?

What's the meaning of the function's non derivable point? Why does an image have a fold that is a non derivable point?

Differentiability means that there is only one tangent at this point, and the position of fold can be said to have no tangent or countless tangents, so it must not be differentiable

(equation required)
(1) The fastest cheetah can run 110 kilometers per hour, 10 kilometers less than the elephant's three times. How many kilometers can the elephant run?
(2) There are the same number of red balls and yellow balls in the bag. Eight red balls and five yellow balls are taken out each time. How many times have the red balls gone and nine yellow balls left? How many red balls and yellow balls were there in the bag?
They all need equations! (what about the second question? Why is there only the first one!)

Let the speed of the elephant be x km / h
3x=110+10
3x=120
x=120×3
x=40
Let's take x times
8x=5x+9
3x=9
x=3
Red ball: 3 × 8 = 24 yellow ball: 3 × 5 + 9 = 24
A: three times, the red ball is gone, and the yellow ball is nine
There were 24 red balls and 24 yellow balls in the bag