Question

What are the possible values of x? 2 possible values :)

Answer 1

Answer:

x = 3, x = 11

Step-by-step explanation:

Since PR is an angle bisector then it divides the opposite side into segments which are proportional to the other 2 sides, that is

$\frac{PQ}{PS}$ = $\frac{QR}{SR}$ , substitute values

$\frac{x+1}{16}$ = $\frac{x-2}{x+1}$ ( cross- multiply )

(x + 1)(x + 1) = 16(x - 2) ← expand left side using FOIL

x² + 2x + 1 = 16x - 32 ( subtract 16x - 32 from both sides )

x² - 14x + 33 = 0 ← in standard form

(x - 3)(x - 11) = 0 ← in factored form

Equate each factor to zero and solve for x

x - 3 = 0 ⇒ x = 3

x - 11 = 0 ⇒ x = 11