Q. 43.7( 3 Votes )

The difference of

Answer :

Let larger number be x and smaller number be y.

Given:


(Large Number)2 – (Smaller Number)2 = 45


x2 – y2 = 45


y2 = x2 – 45


Also Smaller Number2, y2 = 4 × Large Number


x2 – 45 = 4x


x2 – 4x – 45 = 0


On factorizing the above equation,


Sum = -4


Product = -45


Therefore the two numbers satisfying the above conditions are -9 and 5.


x2 – 9x + 5x – 45 = 0


x(x – 9) + 5(x – 9) = 0


(x – 9) (x + 5) = 0


Solving first part,


x – 9 = 0


x = 9


Solving second part,


x + 5 = 0


x = -5


If x = 9, then


y2 = 4 × 9


y2 = 36


y =± 6


If x = -5, then


y2 = 4 × -5


y2 = -20


Value of y becomes imaginary which is not possible.


So possible values of x and y are 9, 6 or 9, -6.


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