Question

Let x_1,x_2 and x_3 be the solutions of the equation 2x^3-x^2+2x-5=0 Without solving the equation, find the sum of the reciprocal values of the solutions of the given equation.

Answer 1

Given :  2x³-x²+2x-5=0  

x₁ , x₂ and x₃  are solution of equation

To Find : the sum of the reciprocal values of the solutions

Solution:

x₁ , x₂ and x₃  are solution of equation

sum of the reciprocal values

= 1/x₁  + 1/x₂   +  1/x₃

= ( x₂x₃ + x₁ x₃ + x₁ x₂)/x₁ x₂x₃

 2x³-x²+2x-5=0  

x₁  + x₂   +  x₃  = - (-1)/2 = 1/2

x₁ x₂  + x₂x₃ + x₁ x₃    = 2/2 = 1

x₁ x₂x₃  = - (-5)/2 = 5/2

( x₂x₃ + x₁ x₃ + x₁ x₂)/x₁ x₂x₃   =       1 / (5/2)   = 2/5

=> 1/x₁  + 1/x₂   +  1/x₃ = 2/5

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