Question

find the roots of the equation 1 by 2 x minus 3 + 1 by x minus 5 is equal to 1​

Answer 1

Roots of the Equation is :

Equation : 1/2x-3 + 1/x-5 = 1

• Cross multiplying and taking LCM

x - 5 + 2x - 3 / (2x-3)(x-5) = 1

3x - 8 = (2x - 3)(x - 5)

3x - 8 = 2x^2 -13x +15

2x^2 - 16x +23 = 0

• Using quadratic formula,

x = - B ± √ B2-4AC / 2A

B = -16, A = 2, C = 23

x = -(-16) ± √ (-16)^2 - 4×2×23 / 4

x = 16 ± √ 256 - 184 / 4

x = 16 ± √ 72 / 4

• x = 4 ± 3/2√2