Question

(p-q),(p^2-q^2),(p^2-pq+q^2) forth proportion​

Answer 1

Question :-

• Find the fourth proportion (p - q), (p² - q²), (p² - pq + q²).

Answer

Given :-

• 4 numbers are in proportion, 3 of them are (p - q), (p² - q²), (p² - pq + q²).

To Find :-

• Fourth proportionate number.

Concept used :-

• If a, b, c, d are in proportion,
• ⇛ a : b :: c : d
• ⇛ ad = bc

Solution :-

Let fourth number be 'x', so that

(p - q), (p² - q²), (p² - pq + q²), x are in proportion.

⇛ (p - q) : (p² - q²) :: (p² - pq + q²) : x

⇛ (p - q) × x = (p² - q²) × (p² - pq + q²)

⇛ (p - q) × x = (p - q)(p + q)(p² - pq + q²)

⇛ x = (p + q)(p² - pq + q²)

⇛ x = p³ + q³

$\bf\implies \:Fourth \: number, \: x = p³ + q³$

Answer 2

Answer:

this is correct.......................