SOLUTION: PLEASE SHOW ME HOW DID YOU GET THE ANSWER TO THIS - 1) The sum of two numbers is 18. And the sum of their squares is 170. Find the numbers

Algebra ->  Problems-with-consecutive-odd-even-integers -> SOLUTION: PLEASE SHOW ME HOW DID YOU GET THE ANSWER TO THIS - 1) The sum of two numbers is 18. And the sum of their squares is 170. Find the numbers      Log On


   

Question 565388: PLEASE SHOW ME HOW DID YOU GET THE ANSWER TO THIS - 1) The sum of two numbers is 18. And the sum of their squares is 170. Find the numbers
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Call numbers +a+ and +b+
given:
(1) +a+%2B+b+=+18+
(2) +a%5E2+%2B+b%5E2+=+170+
-------------------
(1) +b+=+18+-+a+
Substitute this into (2)
(2) +a%5E2+%2B+%28+18+-+a+%29%5E2+=+170+
(2) +a%5E2+%2B+18%5E2+-+36a+%2B+a%5E2+=+170+
(2) +2a%5E2+-+36a+%2B+18%5E2+-+170+=+0+
(2) +2a%5E2+-+36a+%2B+324+-+170+=+0+
(2) +2a%5E2+-+36a+%2B+154+=+0+
(2) +a%5E2+-+18a+%2B+77+=+0+
(2) +a%5E2+-+18a+=+-77+
complete the square
(2) +a%5E2+-+18a+%2B+%2818%2F2%29%5E2+=+-77+%2B+%2818%2F2%29%5E2+
(2) +a%5E2+-+18a+%2B+81+=+-77+%2B+81+
(2) +%28+a+-+9+%29%5E2+=+2%5E2+
Take the square root of both sides
(2) +a+-+9+=+2+
(2) +a+=+11+
and, since
(1) +b+=+18+-+a+
(1) +b+-+18+-+11+
(1) +b+=+7+
The numbers are 11 and 7
check:
(2) +a%5E2+%2B+b%5E2+=+170+
(2) +11%5E2+%2B+7%5E2+=+170+
(2) +121+%2B+49+=+170+
(2) +170+=+170+
OK