Question

plz answer question no. 25 i will mrk u brainliest​

Answer 1

Answer:

6 and 0

Step-by-step explanation:

              x = 1 - √2

⇒ 1 / x = 1 / ( 1 - √2 )

     Multiply as well as divide RHS by ( 1 + √2 ) :

⇒ 1 / x = ( 1 + √2 ) / ( 1 - √2 )( 1 + √2 )

      Using ( a - b )( a + b ) for denominator of RHS

⇒ 1 / x = ( 1 + √2 ) / [ 1^2 - √2^2 ]

⇒ 1 / x = ( 1 + √2 ) / ( 1 - 2 )

⇒ 1 / x = ( 1 + √2 ) / ( - 1 )

⇒ 1 / x = - 1 - √2

         Therefore,

⇒ x + 1 / x

⇒ 1 - √2 + ( - 1 - √2 )

⇒ 1 - √2 - 1 - √2

⇒ - 2√2

   ⇒ x + 1 / x = - 2√2

⇒ ( x + 1 / x )^2 = ( - 2√2 )^2

⇒ x^2 + 1 / x^2 + 2( x * 1 / x ) = 8

⇒ x^2 + 1 / x^2 + 2 = 8

⇒ x^2 + 1 / x^2 = 8 - 2 = 6

      x + 1 / x = 0

⇒ ( x + 1 / x )^3 = 0

⇒ x^3 + 1 / x^3 + 3( x + 1 / x ) = 0

⇒ x^3 + 1 / x^3 + 3( 0 ) = 0

⇒ x^3 + 1 / x^3 = 0

Answer 2

$x = \sqrt{2} \\ \frac{1}{x} = \frac{1}{ \sqrt{2} } \\ \frac{1}{x} = \frac{1}{ \sqrt{2} } \times \frac{ \sqrt{2} }{ \sqrt{2} } = \frac{ \sqrt{2} }{2} \\ (x + \frac{1}{x} ) {}^{2} = ( \sqrt{2} + \frac{ \sqrt{2} }{2} ) \\ (x + \frac{1}{x} ) {}^{2} = \frac{2 \sqrt{2} + \sqrt{2} }{2} \\ (x + \frac{1}{x} ) {}^{2} = \frac{3 \sqrt{2} }{2} \\ (x + \frac{1}{x} ) {}^{3} = {x}^{3} + \frac{1}{ {x}^{3} } + 3 \times x \times \frac{1}{x} (x + \frac{1}{x} ) \\ (x + \frac{1}{x} ) {}^{3} + 3 (x + \frac{1}{x} ) = ( \sqrt{2}) {}^{3} + (\frac{ \sqrt{2} }{ 2 } ) {}^{3}$