Question

The diffeence between two number is 16 and their Hcf and Lcm are 4 and 308 respectively. What is the sum of squares of the two numbers?

Answer 1

Heya !!!



Let two numbers be X and Y.






According to question,




X - Y = 16 ------(1)






HCF and LCM of two numbers = 4 and 308.




As we know that,



Product of two numbers = HCF × LCM



X × Y = 4 × 308





X × Y = 1232 -----------(1)






From equation (1) we get,





X - Y = 16






X = ( 16+Y ) ---------(3)




Putting the value of X in equation (2)




X × Y = 1232




( 16+Y) × Y = 1232






Y² + 16Y - 1232 = 0




Y² + 44 Y - 28Y - 1232 = 0



Y ( Y + 44) - 28 ( Y + 44) = 0





( Y + 44) ( Y - 28) = 0




Y = -44 or Y = 28






Putting Y = 28 in equation (3)




X = ( 16+28) = 44



.


Hence,



Two numbers are 44 and 28





Sum of square of two numbers = (44)² + (28)² =




=> 1936 + 784




=> 2720





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