Question

if x^2 + 1/x^2 = 38 then find x^2 - 1/x^2

Answer 1

Step-by-step explanation:

x^2 + 1/x^2 = 38

(x^2 - 1/x^2)²+2(x²)(1/x²) = 38

(x^2 - 1/x^2)² = 38-2

x^2 1/x^2 = √36 = 6..

Answer 2

Answer:

±12√10

Step-by-step explanation:

Given: $x^{2} +\frac{1}{x^{2} } =38$

$(x+\frac{1}{x} )^{2} =x^{2} +\frac{1}{x^{2} } +2$                               $[ (a+b)^{2} =a^{2} +b^{2} +2ab]$

$(x+\frac{1}{x} )^{2} =38+2$

$(x+\frac{1}{x} )^{2} =40$

$(x+\frac{1}{x} )=$ ±√40

$(x+\frac{1}{x} ) =$ ±2√10                                       --------(1)

$(x+\frac{1}{x} )^{2}- (x-\frac{1}{x} )^{2}=4$                               [ $(a+b)^{2} -(a-b)^{2} =4ab$ ]

  40    -   $(x-\frac{1}{x}) ^{2}$  = 4

 $(x-\frac{1}{x}) ^{2}$=  36

$(x-\frac{1}{x}) =$ ± 6                                            ----------(2)

We know that:

$x^{2} -\frac{1}{x^{2} } =(x-\frac{1}{x} )(x+\frac{1}{x} )$

$x^{2} -\frac{1}{x^{2} } =$     ±6  × ±2√10                       [from (1) and (2)]

$x^{2} -\frac{1}{x^{2} } =$ ± 12√10