Question

The sum of two numbers is 7 and the sum of their cubes is 133, find the sum of their squares

Answer 1

Answer:

• The sum of the squares of the number is 29.

Step-by-step explanation:

Given :

• The sum of two numbers = 7

• Sum of their cubes = 133

To find :

• The sum of their squares = ?

Let, the two numbers be a and b,

Then,

a + b = 7 and a³ + b³ = 133,

Now, a + b = 7 ⟹ (a + b) ³ = 7³

⟹ a³ + b³ + 3ab (a+b) = 343

⟹ 133 + 3ab × 7 = 343

⟹ 21ab = 343 - 133

⟹ 21ab = 210

⟹ ab = 210/21

⟹ ab = 10

We know that ( a + b )² = a² + b² + 2ab

⟹ 7² = a² + b² + 2 x 10

⟹ 49 = a² + b² + 20

⟹ a² + b² = 49 - 20 = 29

Hence,

The sum of the squares of the number is 29.

Answer 2

Answer: The ans will be 29..

Step-by-step explanation:

Let the 2 no. be a and b

Given : a + b = 7

a^3 + b^3 = 133

Using ( a + b )^3 formula

a^3 + b^3 +3ab ( a + b ) = ( 7 )^3

133 + 3ab ( 7 ) = 343

3ab × 7 = 343 - 133

21ab = 210

ab = 210/21

ab = 10

Now we will use ( a + b )^2

( a + b )^2 = a^2 + b^2 + 2ab

( 7 )^2 = a^2 + b^2 + 2 × 10

49 = a^2 + b^2 + 20

a^2 + b^2 = 49-20

a^2 + b^2 = 29..

Plzz mark it as brainlist...