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Home » \( x^2 + x^2 + 4x + 4 = 340 \) - Nelissen Grade advocaten

\( x^2 + x^2 + 4x + 4 = 340 \) - Nelissen Grade advocaten

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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#### 2.857
If \( x + \frac{1}{x} = 5 \), find the value of \( x^2 + \frac{1}{x^2}...
Square both sides: \( \left(x + \frac{1}{x}\right)^2 = 25 \)
Expand: \( x^2 + 2 + \frac{1}{x^2} = 25 \)
Subtract 2: \( x^2 + \frac{1}{x^2} = 23 \)
The ratio of the ages of two people is 5:7. In 6 years, the sum of the...
Let the ages be \( 5x \) and \( 7x \).
In 6 years: \( (5x + 6) + (7x + 6) = 78 \)
Simplify: \( 12x + 12 = 78 \) → \( 12x = 66 \) → \( x = 5.5 \)
Younger age: \( 5 \times 5.5 = 27.5 \)

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