Question

the distance between two points (X, 7) and (1, 15) is 10 then find x??????????​

Answer 1

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Answer 2

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${\large{\red{\boxed{\bold{x\:=\:-5,\:7.}}}}}$

☆ By distance formula:-

$\implies \sqrt{(x2 - x1) {}^{2} + (y2 - y1) {}^{2} } = distance \\ \\ \implies \sqrt{(1 - x) {}^{2} (15 - 7) {}^{2} } = 10 \\ \\ \implies \sqrt{(1 - 2x + {x}^{2}) + (8) {}^{2} } = 10 \\ \\ \implies \sqrt{1 - 2x + {x}^{2} + 64 } = 10 \\ \\\implies \sqrt{ {x}^{2} - 2x + 65 } = 10 \\ \\ \implies( \sqrt{x {}^{2} - 2x + 65) {}^{2} } = (10) {}^{2} \\ \\ \implies \: {x}^{2} - 2x + 65 = 100 \\ \\ \implies {x}^{2} - 2x + 65 - 100 = 0 \\ \\ \implies {x}^{2} - 2x - 35 = 0 \\ \\ \implies {x}^{2} - (7 - 5)x - 35 = 0 \\ \\ \implies {x}^{2} - 7x + 5x - 35 = 0 \\ \\ \implies \: x(x - 7) + 5(x - 7) = 0 \\ \\ \implies(x + 5)(x - 7) = 0 \\ \\ \implies \: x = - 5 \: \: or \: \: x = 7$

☆Therefore either x = -5 or x = 7

☆ So the required values of x ate -5 and 7.

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