The largest side of a triangle is 3 times the shortest side and the third side is 2 cm shorter than the longest side. If the perimeter of the triangle is atleast 61 cm, find the minimum length of the shortest side?

Solve the equation \(8+9\sqrt{(3x-1)(x-2)}=3x^2-7x.\)

If \({{{log}_{e}^{x}}\over{b-c}}={{{log}_{e}^{y}}\over{c-a}}={{{log}_{e}^{z}}\over{a-b}},\) show that x^ay^bz^c = 1

If x = 2 is one root x³+ 2x²- 5x - 6 = 0 then find the other roots of the equation

Solve the equation x³+ 5x²-16x-14 = 0. Given x + 7 is a root