You can
put this solution on YOUR website!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
Regards.
praseenakos@yahoo.co.in
(
