Question

Determine the possible smallest value(s) of x.

The smallest possible value of x is ____
The largest possible value of x is ____

Answer 1

x = 5, x = 7

Explanation:

Tangents to a circle from an external point are congruent, that is

x² = 12x - 35 ( subtract 12x - 35 from both sides )

x² - 12x + 35 = 0 ← in standard form

Consider the factors of the constant term (+ 35) which sum to give the coefficient of the x- term (- 12)

The factors are - 5 and - 7, since

- 5 × - 7 = + 35 and - 5 - 7 = - 12, thus

(x - 5)(x - 7) = 0

Equate each factor to zero and solve for x

x - 5 = 0 ⇒ x = 5

x - 7 = 0 ⇒ x = 7

smallest value of x is 5

largest value of x is 7