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Home » Racines : \(x = 2\) et \(x = 3\) - ToelettAPP

Racines : \(x = 2\) et \(x = 3\) - ToelettAPP

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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🔥 Popular Posts

+ 1 + 3 + 5 = 16 \equiv 0 \pmod{8}
Question: What two-digit positive integer is one more than a multiple...
Solution: Let $ x $ be the two-digit number. We are given:
x \equiv 1 \pmod{7}, \quad x \equiv 3 \pmod{5}
We solve this system using the Chinese Remainder Theorem.
Let $ x = 7k + 1 $. Substitute into the second congruence:
7k + 1 \equiv 3 \pmod{5} \Rightarrow 7k \equiv 2 \pmod{5} \Rightarrow...
So $ k = 5m + 1 $, and $ x = 7(5m + 1) + 1 = 35m + 8 $.
We now find a two-digit value of $ x $:
35m + 8 \geq 10 \Rightarrow m \geq 0, \quad 35m + 8 \leq 99 \Rightarro...

📝 Recent Posts

#### Amount after 3 years: $1157.63
A ladder 10 meters long leans against a wall, forming a 60-degree angl...
Using trigonometry, the height \( h \) is given by:
h = L \sin(\theta) = 10 \sin(60^\circ)
\(\sin(60^\circ) = \frac{\sqrt{3}}{2} \approx 0.866\):
h = 10 \times 0.866 = 8.66
#### Height: 8.66 meters
The sum of the first \( n \) terms of an arithmetic sequence is given...
The sum of the first \( n \) terms is \( S_n = 2n^2 + 3n \).
a_n = S_n - S_{n-1}

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