Examine the following solution to π₯ 2 β 2π₯ = β1: π₯(π₯ β 2) = β1 π₯ = β1 or π₯ β 2 = β1 π₯ = β1 or π₯ = 1 Is this method correct? Explain.
QUESTION
Examine the following solution to xΒ²β 2x = β1:
x(x β 2) = β1
x = β1
or x β 2 = β1
x = β1 or x = 1
is this method correct? explain.
ANSWER
The method is not correct
The root of the quadratic equation is because it is a perfect square.
The above method have given two distinct values:
and are not both the roots of quadratic function
When is substituted in the quadratic equation
The method is assumed to be same as
In these case either
This will always be true because:
For
when either is zero, then
But for and the equation can only be true if
Otherwise this method will give invalid roots.
The method also treat the function
as a function with two variables.
In that for
the first and
The second in the expression becomes so that
The method is invalid
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