Question

Anjali has two sons, one being exactly 2 years older than the other. at present, her age is equal to the sum of squares of the ages of her sons. if 6 years hence, her age will be 8 times the present age of her elder son, find their present ages.

Answer 1

Answer:

Step-by-step explanation:

Son = 12 years

Mother = 42 years 

Explanation - 

Six years ago let the son age = x

Mother = x² 

Present ages now:

Son = x + 6

Mother = x²  + 6

3 years later:

Son = x + 6 + 3 = x + 9

Mother =  x²  + 6 + 3 =  x²  + 9

Solving x - 

x²  + 9 = 3(x + 9)

x²  + 9 = 3x + 27

x²  - 3x - 18 = 0

(x - 6)(x + 3) = 0

x = 6 or x = -3

Take x = 6. As the other value is (- value)

Finding their Present age -

Son = x + 6 = 6 + 6 = 12 years.

Mother =  x²  + 6 = (6)² + 6 = 42 years.

Hence : 

Son = 12 years

Mother = 42 years

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Answer 2

Answer:

Step-by-step explanation: