Question

find the roots of x^2-x-(r^2-1)​

Answer 1

Step-by-step explanation:

Given equation is

x²-2x -(r²-1) = 0. 2).

This can be re written as x² -2x -(r+1) (r-1) = 0. 3)

Splitting the middle term, x² +(r-1 -1 -r)x - (r+1)(r-1) = 0. 4) Simplifying, x² + (r-1)x - (r+1)x -(r-1)(r+1) = 0. 5)

Taking the common factors, x(x+r-1) - (r+1)(x+r-1) = 0. 6)

Hence, the zeroes are r+1, 1-r.

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