Government of India allocated some funds for the refugees who came from Bangladesh for their welfare. The fund is equally distributed among each of the families. The fund allocated is represented by x⁴ + x² + 1 and each of the family received an amount of x² - x + 1.
Based on the above information, answer the following :
(i) Find the number of families received the fund by factorising the given expression.
(ii) Find the value of x if the number of family was 13.
(iii) If each of the family received ₹ 1057, then find the positive value of x.

Question

Government of India allocated some funds for the refugees who came from Bangladesh for their welfare. The fund is equally distributed among each of the families. The fund allocated is represented by x⁴ + x² + 1 and each of the family received an amount of x² - x + 1.

Based on the above information, answer the following :

(i) Find the number of families received the fund by factorising the given expression.

(ii) Find the value of x if the number of family was 13.

(iii) If each of the family received ₹ 1057, then find the positive value of x.

KnowledgeBoat · Accepted Answer

(i) Given, Total fund = x4 + x2 + 1 Amount per family = x2 - x + 1 Number of families = = = = x2 + x + 1. Hence, number of families = x2 + x + 1. (ii) Given, If number of families = 13 ⇒ x2 + x + 1 = 13 ⇒ x2 + x - 12 = 0 ⇒ x2 + 4x - 3x - 12 = 0 ⇒ x(x + 4) - 3(x + 4) = 0 ⇒ (x + 4)(x - 3) = 0 x = -4 or x = 3 ∴ x = 3. Hence, x = 3. (iii) Given, If each family received ₹ 1057 ⇒ x2 - x + 1 = 1057 ⇒ x2 - x - 1056 = 0 ⇒ x2 - 33x + 32x - 1056 = 0 ⇒ x(x - 33) + 32(x - 33) = 0 ⇒ (x - 33)(x + 32) = 0 ⇒ (x - 33) = 0 or (x + 32) = 0 ⇒ x = 33 or x = -32 ∴ x = 33. Hence, x = 33.

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