Two positive numbers x and y are such that x > y. If the difference of these numbers is 5 and their product is 24, find :
(i) sum of these numbers.
(ii) difference of their cubes.
(iii) sum of their cubes.

Question

Two positive numbers x and y are such that x > y. If the difference of these numbers is 5 and their product is 24, find :
(i) sum of these numbers.
(ii) difference of their cubes.
(iii) sum of their cubes.

KnowledgeBoat · Accepted Answer

Given, Difference of numbers = 5 and product = 24. Let the two numbers be x and y. ∴ x - y = 5 and xy = 24. (i) By formula, (x + y)² = (x - y)² + 4xy Substituting values we get : ⇒ (x + y)² = 5² + 4 × 24 ⇒ (x + y)² = 25 + 96 ⇒ (x + y)² = 121 ⇒ (x + y) = . Since, numbers are positive so sum cannot be negative. Hence, sum of these numbers = 11. (ii) By formula, ⇒ x³ - y³ = (x - y)³ + 3xy(x - y) ⇒ x³ - y³ = 5³ + 3 × 24 × 5 ⇒ x³ - y³ = 125 + 360 ⇒ x³ - y³ = 485. Hence, difference of cubes of numbers = 485. (iii) By formula, ⇒ x³ + y³ = (x + y)³ - 3xy(x + y) Substituting x + y = 11, we get : ⇒ x³ + y³ = 11³ - 3 × 24 × 11 ⇒ x³ + y³ = 1331 - 792 ⇒ x³ + y³ = 539. Hence, sum of cubes of numbers = 539.

Mathematics

Two positive numbers x and y are such that x > y. If the difference of these numbers is 5 and their product is 24, find :
(i) sum of these numbers.
(ii) difference of their cubes.
(iii) sum of their cubes.

Expansions

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Mathematics

Two positive numbers x and y are such that x > y. If the difference of these numbers is 5 and their product is 24, find :(i) sum of these numbers.(ii) difference of their cubes.(iii) sum of their cubes.

Expansions

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Two positive numbers x and y are such that x > y. If the difference of these numbers is 5 and their product is 24, find :
(i) sum of these numbers.
(ii) difference of their cubes.
(iii) sum of their cubes.

The sum of two numbers is 9 and their product is 20. Find the sum of their :
(i) squares
(ii) cubes.

If 4x² + y² = a and xy = b, find the value of 2x + y.

The expansion of (x - 3y)(x + 5y) is :
x² + 2xy + 15y²
x² + 2xy - 15y²
x² - 2xy + 15y²
x² - 2xy - 15y²