Question

Six years before, the age of mother was
numerically equal to the square of son's age.
Three years hence, her age will be thrice the
age of her son then. Find the present ages of
the mother and son.by quadratic equation ​

Answer 1

Answer:

Let age of son 6 years before be x

then mother's age = x2

then, persent age son =x+6

mothers age =x2+6

After 3 year,

son =x+6+3=x+9

mother =x2+6+3=x2+9

A.T.Q 

x2+9=3(x+9)

x2+9=3x+27

x2−3x−18=0

x2−6x+3x−18=0

x(x−6)+3(x−6)=0

(x+3)(x−6)=0

x=6        (-3 will neglect)

Persent age of mother = x2+6⇒36+6=42

Son = x+6=6+6=12

Answer 2

Answer :

• Present age of son = 12 years
• Present age of mother = 42 years

Given :

• Six years before , the age of mother was numerically equal to the square of son's age
• Three years hence , her age will be thrice the age of her son

To find :

• Present age of the mother and son

Solution :

• 6 years ago, let the son age be x
• Mother's age be x²

Present age :

• Present age of son = x + 6
• Mother's age = x² + 6

After 3 years,

Given that, her age will be thrice the age of her son so ,

• Son age = x + 6 + 3 = x + 9
• Mother's age = x² + 6 + 3 = x² + 9

so ,

• Son age = x + 9
• Mother age = x² + 9

According To Question :

➵ x² + 9 = 3(x + 9)

➵ x² + 9 = 3x + 27

➵ x² - 3x - 18 = 0

➵ x² - 6x + 3x - 18 = 0

➵ x(x - 6) + 3(x - 6) = 0

➵ (x + 3) (x - 6) = 0

➵ x = 6 . other value is - (value)

Now we have to find the present age :

• Present age of son = x + 6 = 6 + 6 = 12 years
• Present age of Mother = x² + 6 = 6² + 6 = 42 years

Hence,

• Present age of son = 12 years
• Present age of mother = 42 years