The difference between two positive numbers is 4 and the difference between their cubes is 316. Find :
(i) their product
(ii) the sum of their squares.

Question

The difference between two positive numbers is 4 and the difference between their cubes is 316. Find : (i) their product (ii) the sum of their squares.

KnowledgeBoat · Accepted Answer

Let two positive numbers be x and y with x y. Given, The difference between two positive numbers is 4 and the difference between their cubes is 316. x - y = 4 and x³ - y³ = 316. (i) Given, ⇒ x - y = 4 Cubing both sides we get : ⇒ (x - y)³ = 4³ ⇒ x³ - y³ - 3xy(x - y) = 64 ⇒ 316 - 3xy × 4 = 64 ⇒ 316 - 12xy = 64 ⇒ 12xy = 316 - 64 ⇒ 12xy = 252 ⇒ xy = = 21. Hence, product of numbers = 21. (ii) Given, x - y = 4 Squaring both sides we get : ⇒ (x - y)² = 4² ⇒ x² + y² - 2xy = 16 ⇒ x² + y² - 2 × 21 = 16 ⇒ x² + y² - 42 = 16 ⇒ x² + y² = 16 + 42 ⇒ x² + y² = 58. Hence, sum of squares = 58.

Mathematics

The difference between two positive numbers is 4 and the difference between their cubes is 316. Find :
(i) their product
(ii) the sum of their squares.

Expansions

Related Questions

In each of the following, find the value of 'a' :
(i) 4x² + ax + 9 = (2x + 3)²
(ii) 4x² + ax + 9 = (2x - 3)²
(iii) 9x² + (7a - 5)x + 25 = (3x + 5)²

Mathematics

The difference between two positive numbers is 4 and the difference between their cubes is 316. Find :(i) their product(ii) the sum of their squares.

Expansions

Related Questions

In each of the following, find the value of 'a' :(i) 4x2 + ax + 9 = (2x + 3)2(ii) 4x2 + ax + 9 = (2x - 3)2(iii) 9x2 + (7a - 5)x + 25 = (3x + 5)2

The difference between two positive numbers is 4 and the difference between their cubes is 316. Find :
(i) their product
(ii) the sum of their squares.

In each of the following, find the value of 'a' :
(i) 4x² + ax + 9 = (2x + 3)²
(ii) 4x² + ax + 9 = (2x - 3)²
(iii) 9x² + (7a - 5)x + 25 = (3x + 5)²