Question

2x - 2/x = 6 ; x is not = 0, find the roots

Answer 1

by taking 2 common in L.HS and arranging them we get x^2 -1 = 3x
by transpose we get
x^2 - 3x-1=0
by ShriDharaCharya Method
x= {3+(9+4)^1/2}/2 or {3-(9+4)^1/2}/2

Answer 2

solution:

Given, 2x - 2/x = 6 ---------(i), ( since x != 0 )

or, 2x^2 - 2 = 6x, (After multiplication by x both side)

or, 2x^2 - 6x - 2 = 0 (Divide both side by 2)

or, x^2 - 3x - 1 = 0

either x = (-b + D)/2a or (-b - D)/2a

here, a = 1, b = - 3, c = -1

D = ✓[b^2 - 4ac]
D = ✓[9 + 4]
D = ✓13

so, x = (3 + ✓13) / 2 or (3 - ✓13) / 2