the sum of the lives of the two electric lamps, one C.F.L. and other an ordinary lamp is 10 years. The productof the lives of these two lamps is 26 years. Is, this situation possible, if so determine their lives.

Answer :

Life of C.F.L. = x
And
Life of Ordinary lamp  = y  , And we get from first condition given in question  :

x  + y    = 10                           ---------- ( 1 )

And
from second condition , we get

xy  =  26                                    ----------------- ( 2 )

From equation 1 we get y  = 10 - x , Substitute that value in equation 2 , we get

x ( 10 - x ) = 26

10x  - x²  = 26

x² - 10x + 26 = 0

here

b² - 4ac  =  ( -10 )² -  4 $\times$ 1 $\times$ 26  =  100 -  104   = - 4  
So,
b² - 4ac  < 0 
So,
There will be imaginary roots .

So we can say given situation is not possible .                               ( Ans )