Let x1, x2 , x3 be the roots of the equation x3 + 3x + 5 = 0 - Vedic Math - Squares and Cubes

Question

Let x1 , x2 , x3 be the roots of
the equation x3 + 3x + 5 = 0 What is the value of the
expression =>>>

(x1 + ( 1 / x1 )) + ( x2 +
(1/x2 ) ) + (x3 + (1/x3 ))

Rishabh Mittal · Accepted Answer

Dear Student ,

Please find below the solution to the asked query :

x1 , x2 and x3 are the zeroes of x3+3x+5=0x3+0
x2+3x+5=0Now,x1+x2+x3=-coefficient of x2coefficient of x3=-01=0x1x2+x2x3+x3x1=coefficient of xcoefficient of x3=31=3x1x2x3=-constant termcoefficient of x3=-51=-5Now,x1+1x1+x2+1x2+x3+1x3=x1+x2+x3+1x1+1x2+1x3=0 + x2x3+x1x3+x1x2x1x2x3                    Since x1+x2+x3=0=3-5                                                        Sincex2x3+x1x3+x1x2=3 and x1x2x3=-5=-35   ANS
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Let x1 , x2 , x3 be the roots of the equation x3 + 3x + 5 = 0 . What is the value of the expression =>>> (x1 + ( 1 / x1 )) + ( x2 + (1/x2 ) ) + (x3 + (1/x3 ))

Let x₁ , x₂ , x₃ be the roots of the equation x³ + 3x + 5 = 0 . What is the value of the expression =>>>

(x₁ + ( 1 / x₁ )) + ( x₂ + (1/x₂ ) ) + (x₃ + (1/x₃))