Two numbers 17

The sum of two numbers is 9, and the sum of their cubes is 189; find the sum of their squares.

Correct answer:

s =  41

Step-by-step explanation:

a+b=9 a3+b3=189  (a+b)2= 9² a2 + b2 + 2ab= 81  a3+b3=(a+b)( a2+b2ab)= 189 (a+b)( a2+b2ab)= 189 9 ( a2+b2ab)= 189  a2+b2ab = 189/9 = 21 ab= a2 + b2 21  a² + b² +2( a² + b² 21) = 81 3a2 + 3b²  42 = 81 3a2 + 3b² = 81+42 = 123 3(a2+b2) = 123 a² + b² =123/3=41  s=41



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