Question

x
$x2 - 5 |x| + 6 = 0$
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Answer 1

Question :

Solve for x in the given equation ;

x² - 5|x| + 6 = 0

Answer :

x = ±2 , ±3

Solution :

Here ,

The given equation is ;

x² - 5|x| + 6 = 0

The given equation can be rewritten as ;

|x|² - 5|x| + 6 = 0 [ °•° x² = |x|² ]

Now ,

Putting |x| = y , the above equation will become ;

y² - 5y + 6 = 0

Clearly ,

The above equation is quadratic in y .

Now ,

=> y² - 5y + 6 = 0

=> y² - 2y - 3y + 6 = 0

=> y(y - 2) - 3(y - 2) = 0

=> (y - 2)(y - 3) = 0

=> Either (y - 2) = 0 or (y - 3) = 0

• If (y - 2) = 0 , then

=> y = 2

=> |x| = 2

=> x = ±2

• If (y - 3) = 0 , then

=> y = 3

=> |x| = 3

=> x = ±3

Hence ,

x = ±2 , ±3