If \(8 < x < 9\), then \(8^2 < x^2 < 9^2\).
Simplify to get: \(64 < x^2 < 81\)

Since \(x^2 = (10 – y)(10 + y)\), we can substitute this value into the above inequality to get: \(64 < (10 – y)(10 + y) < 81\)
Expand to get: \(64 < 100 – y^2 < 81\)
Subtract \(100\) from all sides to get: \(-36 < –y^2 < -19\)
Multiply all sides by \(-1\) to get: \(36 > y^2 > 19\) [since we multiplied all sides of the inequality by a NEGATIVE value, we REVERSED the direction of the inequality symbols]

At this point, we can easily see that \(y = 5\) satisfies the inequality \(36 > y^2 > 19\)

Answer: E

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8 < x < 9

\(X^2\) = (10 - y)(10 + y)

\(X^2\) = \(10^2\) - \(y^2\)

X = √(\(10^2\) - \(y^2\))

Substitute value given in answer option, for correct option it has to be in between 8 and 9.

Random substitute (E)

X = √(\(10^2\) - \(5^2\))

X = √(100 - 25) = √75

(8^2 = 64 and 9^2 = 81)
75 Value lies between \(8^2\) and \(9^2\)

Correct Option E

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