Question
The sum of two numbers is 17 while the sum of their
squares is 157. Find the sum of the cubes of those two numbers.Solution
Let the number is a and b. ATQ- a+b =17 a2+b2 =157 (a+b)2 = a2+b2 +2ab. 17×17 =157+2ab 2ab =289-157=132. ab =66 (11,6) is the prime factor of 66. So, a=11, and b =6 Now, a3+b3=1331+216=1547.
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