Month: May 2025

$\frac{15}{x^2-3x+4}+ \frac{7}{x^2+7x}+ \frac{10}{x^2+4x-21}+1=0$ Problem: Find the real values of \( x \) satisfying: \[ \frac{15}{x^2 – 3x + 4} + \frac{7}{x^2 + 7x} + \frac{10}{x^2 + 4x – 21} + 1 = 0 \] Solution: Let us consider the expression: \[ \frac{15}{x^2 – 3x + 4} + \frac{7}{x^2 + 7x} + \frac{10}{x^2 + 4x – …

Find the real values of x : Read More »

Detailed Solution: We are given: \(\sqrt[3]{x} + \sqrt[3]{y} = 13 \quad \text{(1)}\) \(\sqrt{x} + \sqrt{y} = 35 \quad \text{(2)}\) Let \( a = \sqrt[6]{x} \) and \( b = \sqrt[6]{y} \). Then: \( \sqrt[3]{x} = a^2 \), \( \sqrt[3]{y} = b^2 \) \( \sqrt{x} = a^3 \), \( \sqrt{y} = b^3 \) Substituting into (1) …

If : $\sqrt[3]{x}+ \sqrt[3]{y} = 13$$\sqrt{x}+ \sqrt{y} = 35$ Find x and y. Read More »

Counting Digit 5 from 1 to 1000 📊 How Many Times Does Digit 5 Appear from 1 to 1000? 🔍 Step-by-Step Breakdown We analyze numbers from 000 to 999 (including leading zeros for consistency), and then separately check 1000. 1️⃣ Units Place In every 10 numbers, digit 5 appears once in the units place. 1000 …

The number of times the digit 5 will appear writing the integers from 1 to 1000 ? Read More »