Question 24

Five times a positive integer is 3 less than twice its square. Find the integer.

Solution

Five times a positive integer is 3 less than twice its square.

$$2I^2 -5I =3$$

this forms a quadratic equation

lcm of 3 and 2 = 6

$$2I^2 -5I -3$$

$$2I^2 -6I+I-3 $$ (middle term factorization)

$$2I(I-3)+1(I-3)$$

I =3 , I = $$\frac{-1}{2}$$

integer must be positive so I =3

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