Question

Find the value of x number on top is 6 and other is 9

Answer 1

x = - 12, 3

Explanation:

By tangent secant theorem:

`x(x + 9) = {6}^(2) \\ \\ {x}^(2) + 9x = 36 \\ \\ {x}^(2) + 9x - 36 = 0 \\ \\ {x}^(2) + 12x - 3x - 36 = 0 \\ \\ x(x + 12) - 3(x + 12) = 0 \\ \\ (x + 12)(x - 3) = 0 \\ \\ x + 12 = 0, \: \: x - 3 = 0 \\ \\ x = - 12, \: \: x = 3 \\ \\`