Question

if x =3-2root2 then find x2+1/x2​

Answer 1

Answer:

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Step-by-step explanation:

Given, x =3-2√2

then, x²+(1/x²) =  (3-2√2)² + [1/ (3-2√2)²] = { [ (3-2√2)²]² + 1 } / (3-2√2)²

  [(x²)² + 1] / x² = { [3² - 2*3*2√2 + (2√2)²]² + 1 } /  [3² - 2*3*2√2 + (2√2)²]

                       = { [9 - 12√2 + 4*(√2)²]² + 1 } / [9 - 12√2 + 4*(√2)²]

                       = { [9 - 12√2 + 4*2]² + 1 } / [9 - 12√2 + 4*2]

                       = { [9 - 12√2 + 8]² + 1 } / [9 - 12√2 + 8]

                       = { [17 - 12√2 ]² + 1 } / [17 - 12√2 ]

                       = { [(17)² - 2*2√2*17 + (2√2)²] + 1 } / [17 - 12√2 ]

                       = { [289 - 68√2 + 4*2] + 1 } / [17 - 12√2 ]

                       = { 289 - 68√2 + 8 + 1 } / [17 - 12√2 ]

                       = { 298 - 68√2 } / [17 - 12√2 ]

using calculator

x2+1/x2​           = 6856.39682

                   

Answer 2

Answer:

$x^{2} + \frac{1}{x^{2} } = 34$

Step-by-step explanation:

GIVEN :    $x = 3 - 2\sqrt{2}$

TO FIND:    $x^{2} + \frac{1}{x^{2} }$

FORMULA USED: $(a + b)^{2} = a^{2} + b^{2} + 2ab\\(a - b)^{2} = a^{2} + b^{2} - 2ab$

$x^{2} + \frac{1}{x^{2} } + 2*x*\frac{1}{x} - 2*x*\frac{1}{x} \\\\(x + \frac{1}{x} )^{2} - 2\\\\(\frac{x^{2} + 1 }{x} )^{2} - 2\\\\(\frac{(3 - 2\sqrt{2} )^{2} + 1 }{3 - 2\sqrt{2} } )^{2} - 2\\\\\frac{((9 + 8 - 12\sqrt{2}) + 1 )^{2} }{9 + 8 - 12\sqrt{2} } - 2\\\\\frac{(18 - 12\sqrt{2})^{2} }{17 - 12\sqrt{2} } - 2\\\\\frac{(6(3 - 2\sqrt{2}))^{2} }{17 - 12\sqrt{2} } - 2\\\\\frac{36(17 -12\sqrt{2}) }{17 - 12\sqrt{2} } - 2\\\\36 - 2 => 34$