Question

if x=3-2√2, find x-1/x

Answer 1

Answer:

Two forces of magnitudes 3P and 2P respectively have a resultant R. If the first force is doubled, the magnitude of the resultant is also doubled. Find the angle between the forces.

Step-by-step explanation:

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Answer 2

Step-by-step explanation:

Given : The value of  $x=3-2\sqrt{2}$.

To find : The value of $x-\frac{1}{x}$

• Formula used :

$(a-b)^{2} =a^{2} +b^{2} -2ab$

• Calculation for $x-\frac{1}{x}$

We have the value of x which is,

$x=3-2\sqrt{2}$

we have to find the value of,

⇒  $x-\frac{1}{x}$

simplified term is,

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

we simply substitute the value of x in equation (1),

⇒  $\frac{x^{2} -1}{x}$  

⇒  $\frac{(3-2\sqrt{2} )^{2} -1}{(3-2\sqrt{2})}$

by using formula we can write $(3-2\sqrt{2} )^{2}$  as,

here $a=3$   and  $b=2\sqrt{2}$

$(3-2\sqrt{2})^{2}=(3)^{2} +(2\sqrt{2})^{2} -2*3*(2\sqrt{2})$

                 $=9+8-12\sqrt{2}$

                 $=17+12\sqrt{2}$

now the fraction is,

⇒  $\frac{17+12\sqrt{2}-1}{3-2\sqrt{2} }$

⇒  $\frac{16+12\sqrt{2}}{3-2\sqrt{2} }$

⇒  $\frac{4(4+3\sqrt{2})}{(3-2\sqrt{2}) }$

Hence we get the answer is $\frac{4(4+3\sqrt{2})}{(3-2\sqrt{2}) }$.