Question

Please help me find x if you have done geometry or are in geometry

Answer 1

x = 5

Explanation:

By the property of intersecting chords inside a circle:

`(x - 2)(x + 7) = 4(2x - 1) \\ \\ {x}^(2) + 7x - 2x - 14 = 8x - 4 \\ \\ {x}^(2) + 5x - 14 - 8x + 4 = 0 \\ \\ {x}^(2) - 3x - 10 = 0 \\ \\ {x}^(2) - 5x + 2x - 10 = 0 \\ \\ x(x - 5) + 2(x - 5) = 0 \\ \\ (x + 2)(x - 5) = 0 \\ \\ x + 2 = 0 \: \: or \: \: x - 5 = 0 \\ \\ x = - 2 \: \: or \: \: x = 5 \\ \\ \because \: length \: can \: not \: be \: - ve \\ \\ \therefore \: x \\eq - 2 \\ \\ \implies \: x = 5`