The difference between two positive numbers is 4 and the difference between their cubes is 316

Question 8 Exercise 4(D)

Answer:

Given difference between two positive numbers is 4 and difference

between their cubes is 316.

Let the positive numbers be a and b

a - b = 4

a³ - b³ = 316

Cubing both sides,

(a - b)3 = 64

a³ - b³ - 3ab(a - b) = 64

Given a³ - b³ = 316

So 316 - 64 = 3ab(4)

252 = 12ab

So ab = 21; product of numbers is 21

Squaring both sides, we get

(a - b)² = 16

a² + b² - 2ab = 16

a² + b² = 16 + 42 = 58

Sum of their squares is 58.

Video transcript

"hello students welcome to leader learning question answer video solutions my name is beljut kaur and i'm your mathematics tutor so let's get started so today's problem is the difference between two positive number is four that means we have no idea so can i say that the difference between two positive number is four and the difference between the cubes that means a cube minus b cube is 316 and these things are given we have to figure out their product and some of their suppliers oh that sounds a little tricky but we have the identities so a minus b whole cube is equals to 4 q that means i have cubed the first equation leaving us with a cube minus b cubed minus of 3 a b a minus b which is equals to 64. now see students we have the value for a cube minus b cube as 316 and a minus b is 4 so let's put it up 316 minus of 3 a b and a minus b is 4 which is equals to 64. on further simplification we can write it as minus of 12 a b is equals to 64. minus of 316 or you can say minus of 12 a b is equals to negative of 252 or in simple version a b is equals to 21 now that's the answer to the first part now coming to the second part they want to know what is the value of the sum of the square so a minus b whole square which is equals to four square because they want to know the sum of their squares so a square plus b square minus of 2 a b is equals to 16. we want to figure out the value of a square plus b square leave this thing as it is a b we just figured it out that is 21. so a square plus b square is equals to 16 plus 42 which is equals to 58 so that's the answer of a square plus b square thank you so much for watching the video kids if you have any questions any queries please drop down in the comment section for more fun videos subscribe to leto have a wonderful day guys"

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The difference between two positive numbers is 4 and the difference between their cubes is 316.
Find : Their product

Given difference between two positive numbers is 4 and difference between their cubes is 316.Let the positive numbers be a and ba - b = 4

a3 - b3 = 316

(a - b)3 = 64

Given a3 - b3 = 316So 316 - 64 = 3ab(4)252 = 12ab

So ab = 21; product of numbers is 21

Concept: Expansion of Formula

  Is there an error in this question or solution?

Page 2

The difference between two positive numbers is 4 and the difference between their cubes is 316.
Find : The sum of their squares

Given difference between two positive numbers is 4 and difference between their cubes is 316.Let the positive numbers be a and ba - b = 4                         .....(1)

a3 - b3 = 316                  .....(2)

Squaring(eq 1) both sides, we get
(a - b)2 = 16
a2 + b2 - 2ab = 16
a2 + b2 = 16 + 42 = 58
Sum of their squares is 58.

Concept: Expansion of Formula

  Is there an error in this question or solution?

The difference between two positive numbers is 4 and the difference between their cubes is 316.
Find : The sum of their squares

Given difference between two positive numbers is 4 and difference between their cubes is 316.Let the positive numbers be a and ba - b = 4                         .....(1)

a3 - b3 = 316                  .....(2)

Squaring(eq 1) both sides, we get
(a - b)2 = 16
a2 + b2 - 2ab = 16
a2 + b2 = 16 + 42 = 58
Sum of their squares is 58.

Concept: Expansion of Formula

  Is there an error in this question or solution?