Question

if the difference between two natural number is 4 and the sum of their square is 58 then the sum of smaller number and the square of the 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

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