Rewrite as x^2 + 11x + 6 = 0
u / v + v / u = [ u^2 + v^2 ] / [ uv ]
By Vieta
u + v = -11 square both sides
u^2 + 2uv + v^2 = 121
u^2 + v^2 =121 - 2uv (1)
Also
uv = 6
So
2uv = 12 (2)
Using (1) and (2)
u/v + v/u = [ u^2 + v^2 ] / [ uv] = [ 121 - 2uv ] / [ uv] = [121 - 12] / 6 = 109 / 6
Here :
https://web2.0calc.com/questions/trapezoid_21
Step 1- reflected in x axis (x ,y) ⇒ (x , -y)
Step 2 - rotated 90° counterclockwise = (x, -y) ⇒ (- -y , x) ⇒ ( y, x)
Step 3 -reflected in the line y = x = (y , x) ⇒ ( x , y) = image point
Nice, Anthrax !!!!
https://web2.0calc.com/questions/thank-you-please-help
(4x)/ 8 = y .......so.....
(4x) / 8 = 3
(1/2)x = 3
x = 3 / (1/2) = 6
Formula for the nth Lucas number =
Lucas(n) = Phi^n + ( –phi )^n
Where Phi = (1 + sqrt 5)/ 2
And phi = ( sqrt 5 - 1 ) / 2
L (100) = [ (1 + sqrt 5)/2 ]^100 + [ (-1)( sqrt 5 - 1)/2 ]^100 = 792070839848372253127
3x^2 + 7x + k = 0
Let the roots be a and b
1/a + 1/b = 7/3
(a + b) / ab = 7/3
The product of the roots = k/3
ab = k/3
(a + b) / (k/3) = 7/3
3 (a + b) = (7/3)k
a + b = (7/9)k
And the sum of the roots = -7/3
(-7/3) = (7/9)k
k = (-7/3) / (7/9) = -3
Let
a = the width of the the top left rectangle
b = its height
c = the height of the bottom left rectangle
d = the width of the top rght rectangle
Then x = dc
ab = 3 ab = 3
ac = 7 db =12
b : c = 3 : 7 a : d = 3 : 12 = 1 : 4
Let b + c = 10 Let a + d = 5
Then c = 7 Then d = 4
dc = 4 * 7 = 28 = x
\( $4x^{1/3}-2\frac{x}{x^{2/3}}=7+\sqrt[3]{x}/2$\)
4x^(1/3) - 2x^(1/3) = 7 + x^(1/3) / 2
2x^(1/3) = 7 + x^(1/3) / 2 multiply through by 2
4x^(1/3) = 14 + x^(1/3)
3x^(1/3) = 14
x^(1/3) = 14 / 3 cube both sides
x = (14/ 3)^3 = 2744 / 27
