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Home » The product of two consecutive even integers is 168. Find the smaller integer. - Tacotoon

The product of two consecutive even integers is 168. Find the smaller integer. - Tacotoon

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 D = (x^2 - 2x + 1) + (4x^2 + 16x + 16) = 5x^2 + 14x + 17

📌 \(D' = 10x + 14\). Set to zero:

📌 \(10x + 14 = 0 \Rightarrow x = -rac{7}{5}\)

📌 Then \(y = 2(-rac{7}{5}) + 3 = -rac{14}{5} + rac{15}{5} = rac{1}{5}\)

📌 Thus, the closest point is \(\left(-rac{7}{5}, rac{1}{5}

📌 oxed{\left(-rac{7}{5},\ rac{1}{5}

📌 Question: Find the minimum value of \((\cos x + \sec x)^2 + (\sin x + \csc x)^2\) for \(0 < x < rac{\pi}{2}\).

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But let’s reconsider: perhaps the intended LCM was miscalculated.
Wait: $ \text{lcm}(7,8,9) $:
$ 7 $: prime
$ 8 = 2^3 $, $ 9 = 3^2 $ → coprime to others
So $ \text{lcm} = 7 \cdot 8 \cdot 9 = 504 $, correct.
Hence, no two-digit number satisfies $ x \equiv -3 \pmod{504} $.
The smallest positive solution is $ x = 501 $, which is three-digit.
Therefore, there is **no two-digit** such number.
But perhaps the question meant **three less than a multiple of 7, or 8...
Alternatively, maybe it meant a number such that $ x + 3 $ is divisibl...

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