The sum of (x + 5) observations is x⁴ - 625. Find the mean of the observations.

Solution:

Given, the sum of (x + 5) observations is x⁴ - 625.

Mean = (Sum of observations) ÷ (Number of observations)

= (x⁴ - 625) ÷ (x + 5)

Using standard identity, a² - b² = (a + b) (a - b), (x⁴ - 625) can be written as,

(x⁴ - 625) = (x²)² - (25)²

= (x² + 25) (x² - 25)

= (x² + 25) (x + 5) (x - 5)

∴ (x⁴ - 625) ÷ (x + 5)

= [(x² + 25) (x + 5) (x - 5)] ÷ (x + 5)

= (x² + 25)(x - 5)

✦ Try This: The sum of (a + 5) observation is 2a² + 5a - 25. Find the mean of the observations.

Given, the sum of (a + 5) observations is 2a² + 5a - 25.

Mean = (Sum of observations) ÷ (Number of observations)

= (2a² + 5a - 25) ÷ (a + 5)

= (2a² + 10a - 5a - 25) ÷ (a + 5)

= [2a(a + 5) - 5(a + 5)] ÷ (a + 5)

= [(2a - 5) (a + 5)] ÷ (a + 5)

= 2a - 5

☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 9

NCERT Exemplar Class 8 Maths Chapter 7 Problem 103

The sum of (x + 5) observations is x⁴ - 625. Find the mean of the observation.

Summary:

Given the sum of (x + 5) observations is x⁴ - 625, the mean of the observations is (x² + 25)(x - 5)

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