ax2 + bx + c = 0
To solve this problem, we need to use the formula X1*X2 = c ÷ a
(√3-1) * X2 = 4 ÷ 2
X2 = 2/ √3-1
Using that, we can figure out k,
X1 + X2 = -a/b
(2/√3-1) + (√3-1) = -(-2k/2)
We got k = 2√3
Can someone check over my work? Not sure about the answer, pretty sure the solution is right...
I am not familiar with these problems and don't know how to help you, but here are some ideas...
If you can make the exponent equal to zero on both sides, you could always have a solution.
3^x = 2^x if x = 0, then there is a solution. If the problem says that x is not equal to zero, then I don't know.
I have no idea for the second one.
Assuming that your picture means that the diameter of the smaller square is the radius of the bigger square, here is the solution.
Lets say that the radius of the small circle is x, hence the radius of the larger circle is 2x. Using the area of circles formula: a = πr^2, where r is the radius, the area of the smaller circle is πx^2 and the area of larger circle is 4πx^2
The πx^2 cancels out, leaving us with 1:4.
The simpler solution is that if two shapes are similar, the ratio of their area will be one of the corresponding side's square. In this case, the radius.
The formula to calculate the area of a circle is π*r^2, where r is the radius and pi is 3.14159265358979......
With that said, we could calculate the area of the outer red ring, but we just know the diameter. Since the radius is half the length of the diameter, the area of the ring will be 25π - (8/2)^2π , since the red ring is the different of the two circles.
Using the same logic, the red ring smaller than that is 5π, and the red circle in the middle is 1π. Adding those numbers together, we will get
9π + 5π + π
The answer to this problem is 15π.
I hope this helped,