Question

the harmonic mean of the roots of the equation (root2+1)x^2 -(2+root 3)x-(4+2root3)=0 is

Answer 1

let a and b are the roots of
(√2 +1)x² -( 2 + √3)x -( 4 + 2√3) = 0
sum of roots = a + b = ( 2 +√3)/( √2 +1)
products of roots = ab = -(4+2√3)/(√2+1)


harmonic mean of roots = 2ab/( a + b)
= -2(4 +2√3)/(√2+1)/(2 +√3)/(√2+1)
= -2×2( 2+√3)/(2+√3)
= -4

Answer 2

Step-by-step explanation:

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