Question

Find the values of x

Answer 1

x = 4

Explanation:

In circle with centre C, AB and AD are tangents from external point A.

AB = AD (tangents from external point to a circle are equal)

`\implies \: 2 {x}^(2) + 2x = 7x + 12 \\ \\ \implies \: 2 {x}^(2) + 2x - 7x - 12 = 0 \\ \\ \implies \: 2 {x}^(2) - 5x - 12 = 0 \\ \\ \implies \: 2 {x}^(2) - 8x + 3x - 12 = 0 \\ \\ \implies \: 2x( {x} - 4) + 3(x - 4)= 0 \\ \\ \implies \: ( {x} - 4) (2x + 3)= 0 \\ \\ \implies \: x - 4 = 0 \: \: 2x + 3 = 0 \\ \\ \implies \: x = 4 \: or \: x = - (3)/(2) \\ \\ \because \: x \\eq \: - ve \\ \\ \implies \: x = 4`