A root problem

Algebra Level 2

Given the equation below ( m m is the parameter):

x 2 − x ( m − 1 ) − m = 0 x^{2} -x(m-1)-m=0

We find that a solution to this equation is 2 2 . Find another real solution x n x_{n} of this equation and m m . Type x n + m x_{n} + m


The answer is 1.

Tin Le by Tin Le , 15, Vietnam

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

Tom Engelsman
Jul 13, 2019

This quadratic simply factors into:

x 2 − ( m − 1 ) x − m = ( x + 1 ) ( x − m ) = 0 ⇒ x n = − 1 , m = 2 x^2 - (m-1)x - m = (x+1)(x-m) = 0 \Rightarrow x_{n} = -1, m = 2 .

Thus, x n + m = 1 . x_{n} + m = \boxed{1}.

0 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...