THE DIFFERENCE OF SQUARES OF TWO POSITIVE INTEGERS IS 180 AND THE SQUARE OF THE SMALLER NUMBER IS 8 TIMES THE LARGER NUMBER . FIND THE NUMBERS.

Asked by dalbirgolagarh | 30th Nov, 2015, 06:51: PM

Expert Answer:

G i v e n space t h a t space t h e space s q u a r e s space o f space t w o space p o s i t i v e space i n t e g e r s space i s space 180. L e t space x space a n d space y space b e space t w o space p o s i t i v e space i n t e g e r s space s u c h space t h a t comma space x greater than y. G i v e n space t h a t comma x squared minus y squared equals 180... left parenthesis 1 right parenthesis A l s o space w e space h a v e comma space y squared equals 8 x... left parenthesis 2 right parenthesis S u b s t i t u t i n g space t h e space v a l u e space o f space y squared space f r o m space e q u a t i o n space left parenthesis 2 right parenthesis space i n space e q u a t i o n space left parenthesis 1 right parenthesis comma space w e space h a v e comma x squared minus 8 x minus 180 equals 0 rightwards double arrow x squared minus 18 x plus 10 x minus 180 equals 0 rightwards double arrow x open parentheses x minus 18 close parentheses plus 10 open parentheses x minus 18 close parentheses equals 0 rightwards double arrow open parentheses x plus 10 close parentheses open parentheses x minus 18 close parentheses equals 0 S i n c e space x space i s space a space p o s i t i v e space i n t e g e r comma space w e space h a v e comma space x equals 18 S u b s t i t u t i n g space t h e space v a l u e space x equals 18 space i n space e q u a t i o n space left parenthesis 1 right parenthesis comma space w e space h a v e comma 18 squared minus y squared equals 180 rightwards double arrow 324 minus y squared equals 180 rightwards double arrow 324 minus 180 equals y squared rightwards double arrow 144 equals y squared rightwards double arrow y equals 12 T h u s comma space t h e space n u m b e r s space a r e space 18 space a n d space 12.

Answered by Vimala Ramamurthy | 30th Nov, 2015, 07:09: PM

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