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प्रश्न
The sum of (x + 5) observations is x4 – 625. Find the mean of the observations.
उत्तर
We have, the sum of (x + 5) observations = x4 – 625
We know that, the mean of the n observations x1, x2, ... xn is given by `(x_1 + x_2 + ... x_n)/n`.
∴ The mean of (x + 5) observations = `("Sum of" (x + 5) "observations")/(x + 5)`
= `(x^4 - 625)/(x + 5)`
= `((x^2)^2 - (25)^2)/(x + 5)`
= `((x^2 + 25)(x^2 - 25))/(x + 5)` ...[∵ a2 – b2 = (a + b)(a – b)]
= `((x^2 + 25)[(x)^2 - (5)^2])/(x + 5)`
= `((x^2 + 25)(x + 5)(x - 5))/((x + 5))`
= (x2 + 25)(x – 5)
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