This method uses the fact that ab = 0 => a = 0 or b = 0.
Thus x² -3x +2 = 0 => (x -1)(x -2) = 0 => x -1 = 0 or x -2 = 0
=> x = 1 or x = 2. Thus x = 1, x = 2 are roots of the equation x² -3x +2 = 0.
Solve for x: (x +3)(x -3) = 40.
(x +3)(x -3) = 40 => x² -9 = 40
=> x² -49 = 0 => (x -7)(x +7) = 0
=> x -7 = 0 or x +7 = 0 => x = 7 or x = -7.
Hence the roots of the given equation are 7, -7.
Solve(x -3)/(x +3) + (x +3)/(x -3) = 5/2
Given (x -3)/(x +3) + (x +3)/(x -3) = 5/2
To clear the fractions, multiply both sides by L.C.M. of fractions i.e. by 2(x +3)(x -3) to get
2(x -3)² +2(x +3)² = 5(x -3)(x +3)
=> 2(x² -6x +9) +2(x² +6x +9) = 5(x² -9)
=> 2x² -12x +18 +2x² +12x +18 -5x² +45 = 0
=> -x² +81 = 0 => x² -81 = 0 => (x -9)(x +9) = 0
=> x -9 = 0 or x +9 = 0
Hence the values x = 9, x = -9 satisfy the given equation.
Solve the following equations by factorisation: