3x2 + x = x*(3x + 1)
3x/(5-x)/3=4 3x/(5-x)=4X3 3x=12(5-x) 3x=60-12x 3x+12x=60 x=4
(x^2-2) (x^2+3x+5)= x^2(x^2+3x+5) -2(x^2+3x+5)= x^4 +3x^3 +5x^2 -2x^2 -6x -10= x^4 +3x^3 +3x^2 -6x -10
x-2=3x+1 x=3x+1+2 x-3x=3 -2x=3 x=-3/2
0.25 x 3x is 0.75x.
6vx
50 x 3 = 150
3x * (x - 4) = 3x*x - 3x*4 = 3x^2 - 12x.
- 3x - Xsame as- 3x + (- X)= - 4X=====
y = (3x + 1)⁵(3 - x)³ The stationary points are where dy/dx = 0 Note the use of: If u and v are functions of x: d/dx (uv) = v du/dx + u dv/dx d/dx uⁿ = n uⁿ⁻¹ du/dx dy/dx = (3 - x)³ d/dx (3x + 1)⁵ + (3x + 1)⁵ d/dx (3 - x)³ = (3 - x)³ 5 (3x + 1)⁴ d/dx (3x + 1) + (3x + 1)⁵ 3 (3 - x)² d/dx (3 - x) = 5 (3 - x)³ (3x + 1)⁴ 3 + 3 (3x + 1)⁵ (3 - x)² (-1) = 3 (3x + 1)⁴ (3 - x)² (5 (3 - x) - (3x + 1)) = 3 (3x + 1)⁴ (3 - x)² (15 - 5x - 3x - 1) = 3 (3x + 1)⁴ (3 - x)² (14 - 8x) = 6 (3x + 1)⁴ (3 - x)² (7 - 4x) → 3x + 1 = 0 → x = -1/3 or 3 - x = 0 → x = 3 or 7 - 4x = 0 → x = 7/4
(3x2 - 6x)/3x = 3x(x-2)/3x = x-2, for x<>0
3x * (x - 4) = 3x*x - 3x*4 = 3x^2 - 12x.
x^2 + 3x + 2/(-3x) - x^2 - 2=3x-2+2/(-3x)=3x-2-2/(3x)
3x2 + x = x*(3x + 1)
3x/(5-x)/3=4 3x/(5-x)=4X3 3x=12(5-x) 3x=60-12x 3x+12x=60 x=4
If the angles are x, 3x and 3x+5, the following equation gives x x+3x+(3x+5)=180 -> x =25, and in degrees the angles are 25, 75 and 80.
(x^2-2) (x^2+3x+5)= x^2(x^2+3x+5) -2(x^2+3x+5)= x^4 +3x^3 +5x^2 -2x^2 -6x -10= x^4 +3x^3 +3x^2 -6x -10