Given: α,β are zeroes of the polynomial x

2

−4x+1

To find the value of

α

1

+

β

1

−αβ

Sol: From the given quadratic equation,

α+β=4 and αβ=1

Therefore,

α

1

+

β

1

−αβ=

αβ

α+β

−αβ

⟹=4−1=3

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Music is the art of arranging sounds in time to produce a composition through the elements of melody, harmony, rhythm, and timbre. It is one of the universal cultural aspects of all human societies.