Question

3 (x square + 1 /x square) - 4(x-1/x)-6 =0 solve the equation
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Answer 1

Answer :

x = ± 1 , (2 ± √13)/3

Solution :

• Given : 3(x² + 1/x²) - 4(x - 1/x) - 6 = 0

• To find : x = ?

We have ;

=> 3(x² + 1/x²) - 4(x - 1/x) - 6 = 0

=> 3(x² + 1/x² - 2 + 2) - 4(x - 1/x) - 6 = 0

=> 3(x² + 1/x² - 2) + 6 - 4(x - 1/x) - 6 = 0

=> 3(x² + 1/x² - 2) - 4(x - 1/x) = 0

=> 3[ x² + 1/x² - 2•x•(1/x) ] - 4(x - 1/x) = 0

=> 3(x - 1/x)² - 4(x - 1/x) = 0

Let x - 1/x = y , then

=> 3y² - 4y = 0

=> y(3y - 4) = 0

=> y = 0 , 4/3

• If y = 0 , then

=> x - 1/x = 0

=> x = 1/x

=> x² = 1

=> x = √1

=> x = ± 1

• If y = 4/3 , then

=> x - 1/x = 4/3

=> (x² - 1)/x = 4/3

=> 3(x² - 1) = 4x

=> 3x² - 3 = 4x

=> 3x² - 4x - 3 = 0

=> x = [ -(-4) ± √{(-4)² - 4•3•(-3)} ] / 2•3

=> x = [ 4 ± √(16 + 36) ] / 2•3

=> x = [ 4 ± √52 ] / 2•3

=> x = [ 4 ± 2√13 ] / 2•3

=> x = [ 2 ± √13 ] / 3

Hence ,

x = ± 1 , (2 ± √13)/3