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.
(ii) sum of their cubes.
find the value of​

Answer 1

Step-by-step explanation:

equation first is. x-y=5. (x>y)

second equation. is. x×y= 24

now x=y+5 from first

put value of x in equation second

now

(y+5)×(y)=24

y^2 + 5y -24= 0

y^2 + 8y -3y -24= 0

y(y+8)-3(y+8)=0 ( on solving the problem)

(y+8)×(y-3) = 0

now

y+8=0

y=-8 (not possible as no are positive)

so y=3

thus on putting value of y in equation first we get

x-3=5

x =8

thus the two numbers are

x=8

y= 3

I) sum = 11

ii)8^3 - 3^3= 512-27=485

iii) 512+27=539

hope it helps iii

Answer 2

Required Answer :

(i) Sum of these numbers = 11

(ii) Difference of their cubes = 485

(ii) Sum of their cubes = 539

Given :

• Two positive numbers are x and y such that the x > y.

• Difference of the two positive numbers = 5

• The product of the two positive numbers = 24

To find :

(i) Sum of these numbers.

(ii) Difference of their cubes.

(ii) Sum of their cubes.

Solution :

The two positive numbers :

• Greater number = x
• Smaller number = y

According to the first condition given,

⇒ Difference of the two numbers = 5

⇒ x - y = 5 ---------(1)

According to the second condition given,

⇒ The product of the two numbers = 24

⇒ x × y = 24

⇒ xy = 24 --------(2)

Taking equation (1) :

⇒ x - y = 5

⇒ x = 5 + y ---------(3)

Substituting equation (3) in (2) :

⇒ xy = 24

⇒ (5 + y)y = 24

⇒ 5y + y² = 24

⇒ y² + 5y - 24 = 0

A quadratic equation is formed whose product is - 24 y². So, let's solve it.

⇒ y² + 8y - 3y - 24 = 0

⇒ y(y + 8) - 3(y + 8) = 0

⇒ (y - 3)(y + 8) = 0

⇒ (y - 3) = 0 or (y + 8) = 0

⇒ y = 3 or y = - 8

The value y = - 8 will get rejected because it is mentioned in the question that the two numbers are positive.

So, the value of y = 3

Substitute the value of y in equation (1) :

⇒ x - y = 5

⇒ x - 3 = 5

⇒ x = 5 + 3

⇒ x = 8

Therefore, the value of x = 8 and y = 3

(i) Sum of these numbers :-

⇒ x + y

⇒ 8 + 3

⇒ 11

(ii) Difference of their cubes :-

⇒ (8)³ - (3)³

⇒ 512 - 27

⇒ 485

(iii) Sum of their cubes :-

⇒ (8)³ + (3)³

⇒ 512 + 27

⇒ 539