Question

if the difference between two natural numbers is 2 and the sum of their squares is 244 then the sum of the smaller number and the square of the larger number is

Answer 1

small no. =10

big no.=12

10 x 10+12 x 12=244

so, 10+144=154

Answer 2

Given :  difference between two natural numbers is 2 and the sum of their squares is 244,

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

Solution:

Let say Smaller Number = A

Larger Number = A +2

sum of their squares is 58

=> A² + (A + 2)² = 244

=> A² +A² + 4A + 4 = 244

=> 2A² + 4A - 240 = 0

=> A² + 2A - 120 = 0

=> A² + 12A - 10A - 120 = 0

=> A(A +  12) - 10(A +12) = 0

=> (A -10 )(A + 12) = 0

=> A = 10  , A = - 12

A = 10  as Natural numbers

Smaller Number =  10

Larger Number = 10 + 2 = 12

sum of smaller number and the square of larger number is

= 10 + 12²

=10 + 144

= 154

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