Answers to Matched Exercises of Quadratic Equations
That Can be Reduced to the Quadratic Form

Answers to the matched exercises in Tutorial on Equations of the Quadratic Form are presented.

Matched Exercise 1:

Find all real solutions to the equation.
x 4 - 2 x 2 - 3 = 0

Let u = x
2
The above equation may be written as
u
2 - 2 u - 3 = 0
Solve the above for u to obtain the solutions
u = - 1 and u = 3
We now solve for x.
u = x
2 = - 1 , this equation has no real solutions.
u = x
2 = 3 gives x = √3 and x = - √3
The given equation has 2 real solutions.
x3 = √3
x4 = - √3



Matched Exercise 2.

Find all real solutions to the equation.
x - 3 √x - 4 = 0
Let u = √x which gives u2 = x
The given equation is now written in terms of u as follows
u
2 - 3 u - 4 = 0
Solve the above quadratic equation for u to obtain
u = - 1 and u = 4
Solve for x
u = √x = - 1 , this equation has no real solution √x is positive
u = √x = 4 , square both sides to obtain the solution
x = 16

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