Question

If the difference between two natural numbers is four and the sum of their squares is 58, then the sum of smaller number and the square of larger number is

Answer 1

Given :  difference between two natural numbers is four and the sum of their squares is 58,

To Find :  the sum of smaller number and the square of larger number is

Solution:

Let say Smaller Number = A

Larger Number = A + 4

sum of their squares is 58

=> A² + (A + 4)² = 58

=> A² +A² + 8A + 16 = 58

=> 2A² + 8A - 42 = 0

=> A² + 4A - 21 = 0

=> A² + 7A - 3A - 21 = 0

=> A(A +  7) - 3(A + 7) = 0

=> (A -3 )(A + 7) = 0

=> A = 3  , A = - 7

A = 3  as Natural numbers

Smaller Number =  3

Larger Number = 3 + 4 = 7

sum of smaller number and the square of larger number is

= 3 + 7²

= 3 + 49

= 52

Learn More :

Some natural numbers can be written as a difference of two perfect ...

https://brainly.in/question/12911027

https://brainly.in/question/15782377