Question

Find the roots of x^2-2x-(r^2-1)=0​

Answer 1

x  

2

−2x+1=0

To solve the equation, factor x  

2

−2x+1 using formula x  

2

+(a+b)x+ab=(x+a)(x+b). To find a and b, set up a system to be solved.

a+b=−2

ab=1

Since ab is positive, a and b have the same sign. Since a+b is negative, a and b are both negative. The only such pair is the system solution.

a=−1

b=−1

Rewrite factored expression (x+a)(x+b) using the obtained values.

(x−1)(x−1)

Rewrite as a binomial square.

(x−1)  

2

 

To find equation solution, solve x−1=0.

x=1

HERE IS THE GRAPH OF IT

SARANGHAE

BORANGHAE