Find b and then solve the equation: (b−1)x2−(b+1)x=72, if one of its roots is 3

b = 14
roots of the equation are 3 and -24/13

Explanation:
Part (a): getting the value of b:
The given equation is:
(b-1) x² - (b-1) x = 72
This can be rewritten as:
(b-1) x² - (b+1) x - 72 = 0

We are given that:
one of the roots is 3.
This means that if we substituted with x = 3 in the given equation, the final result would be zero.

Substitute with x = 3 and solve for b as follows:
(b-1) x² - (b+1) x - 72 = 0
(b-1) (3)² - (b+1)(3) - 72 = 0
(b-1)(9) - (b+1)(3) - 72 = 0
9b - 9 - 3b - 3 - 72 = 0
6b - 12 - 72 = 0
6b = 12 + 72
6b = 84
b = 14

This means that the equation now is:
(14-1) x² - (14+1) x - 72 = 0
13 x² - 15 x - 72 = 0

Part (b): solving the equation:
To solve the equation means to get the value of its roots.
To do this, we will simply factorize the given equation as follows:
13 x² - 15 x - 72 = 0
(x-3)(13x+24) = 0
This means that:
either x-3 = 0 > x = 3
or 13x + 24 = 0 > x = -24/13

Hope this helps :)