Question 63559
QUESTION:

24 less than the square of a number is five times the number. find all such numbers.

ANSWER:

Suppose the number be,  " x "

Square of that number  = x^2


24 less than the square of the number = x^2 -24

Five times the number  = 5x


Now,24 less than the square of a number = five times the number


==> x^2 -24 = 5x


==> x^2 -24 - 5x = 5x -5x ( subtract 5x from both sides)


==> x^2- 5x -24 = 0


This is a quadratic equation.


We can solve it using splitting the middle term or using quadratic formula.


Method 1:

 

x^2- 8x+3x -24 = 0  (split the middle term so that sum of the numbers is -5 and their product is -24


(x^2- 8x)+(3x -24) = 0 ( group the terms)


x(x-8) + 3(x-8) = 0  ( take out common terms from each group.)


==>( x-8)(x+3)= 0   (since x-8 is common in both terrms, again take it out)


==> either (x-8)=0  or (x+3) = 0


==> x-8=0  ==>x = 8



x + 3 = 0 ==> x = -3


so  the possible numbers are 8 or -3


We can also apply quadratic formula to solve the equation 



{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} 



Regards.

praseenakos@yahoo.co.in