Question

Anjali was born in 1985 A.D. In the year x^2
A.D , she was (x-5) years old. Find the value of x.

Chapter- Quadratic equations.

Answer 1

                    =====================

Given,

Anjali born in 1985 A.D.

In x² A.D. she was of ( x - 5 ) yrs.

So, to get her age in x² A.D. , we have to subtract 1985 A.D. from x² A.D.

⇒ x² - 1985 = ( x - 5 )

⇒ x² - 1985 - x + 5 = 0

⇒ x² - x - 1980 = 0

⇒ x² - 45x + 44x - 1980 = 0

⇒ x ( x - 45 ) + 44 ( x - 45 ) = 0

⇒ ( x - 45 ) ( x + 44 ) = 0

⇒ ( x - 45 ) = 0 / ( x + 44 )

⇒ ( x - 45 ) = 0

∴ x = 45

   Or

⇒ ( x - 45 ) ( x + 44 ) = 0

⇒ ( x + 44 ) = 0 / ( x - 45 )

⇒ ( x + 44 ) = 0

 ∴  x = -44

Therefore x = 45 or -44.

But the age or year can't be in negative , so possible value is 45.


Hope it helps !!

Answer 2

Hey Nancy,

Here is your solution.

Given,

Anjali born in 1985 A.D. and in the x² A.D. she became of ( x - 5 ) yrs old.

So,

The age of Anjali in x² A.D. = ( x² - 1985 ) yrs. ( We won't include A.D. here as we are finding her age ).

Now,

⇒ ( x² - 1985 ) yrs = ( x - 5 ) yrs

yrs and yrs got cancelled.

⇒ x² - x - 1985 + 5 = 0

⇒ x² - x - 1980 = 0

By splitting middle term ,

⇒ x² - 45x + 44x - 1980 = 0

⇒ x ( x - 45 ) +44 ( x - 45 ) = 0

⇒ ( x - 45 ) ( x + 44 ) = 0

⇒ ( x - 45 ) = 0 ÷ ( x + 44 )

⇒ x - 45 = 0

 ∴  x = 45

    " Or "

⇒ ( x - 45 ) ( x + 44 ) = 0

⇒ ( x + 44 ) = 0 ÷ ( x - 45 )

⇒ ( x + 44 ) = 0

 ∴  x = -44.

Here we got that x = either 45 or - 44 but the age of any person can't be negative.

Hence, x = 45.

Points to jot down : Whenever you split the middle term , split it in such a way that its product should be equal to the product of first term and second term , and its sum should be equal to middle term.

Hope it helps !!