If x-3-8 then x2-1-x2 - - a 34 b 56 c 28 d 63

X = 3+√(8) 1/x = 1/ 3+√(8) = 1(3 √(8))/(3+√(8))(3 √(8)) = 3 √(8)/9 8 = 3 √(8) x + 1/x =3+√(8)+ 3 √(8) = 6 (x + 1/x)^2 = 36 x^2 + 1/x^2 + 2 = 36 x^2 + 1/x^2 ...

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Standard IX

Mathematics

Rationalisation

If x=3+√8 the...

Question

If $x = 3 + \sqrt{8}$ then $(x^{2} + \frac{1}{x^{2}})$ = ?

(a) 34 (b) 56 (c) 28 (d) 63

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Solution

$x = 3 + \sqrt{8} \frac{1}{x} = \frac{1}{3 + \sqrt{8}} = \frac{1 (3 - \sqrt{8})}{(3 + \sqrt{8}) (3 - \sqrt{8})} = \frac{3 - \sqrt{8}}{9 - 8} = 3 - \sqrt{8}$

$x + \frac{1}{x} = 3 + \sqrt{8} + 3 - \sqrt{8} = 6$

$(x + \frac{1}{x})^{2} = 36 x^{2} + \frac{1}{x^{2}} + 2 = 36 x^{2} + \frac{1}{x^{2}} = 34$

Hence, the correct answer is option (a)

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Similar questions

Q. If

x = 3 + \sqrt{8} then (x^{2} + \frac{1}{x^{2}}) = ?

(a) 34
(b) 56
(c) 28
(d) 63

Q. If

x = (3 + \sqrt{8})

, show that

(x^{2} + \frac{1}{x^{2}}) = 34

Q. If sin (θ + 34°) = cos θ and θ is acute, then θ = ?
(a) 56°
(b) 66°
(c) 28°
(d) 42°

Q. Assertion :If

x = {(\frac{2}{3})}^{4} \div {(\frac{2}{3})}^{2}

, then value of

x^{2} + 2 x + 3

is 0 Reason: If

{(- \frac{1}{2})}^{4} \times (- 2)^{8} = (- 2)^{4 x}

then x=1.

Q. If

\frac{1}{x^{4} + x^{2} + 1} = \frac{A x + B}{x^{2} + x + 1} + \frac{C x + D}{x^{2} - x + 1}

, then

C + D =

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If x=3+√8 then (x2+1x2) = ? (a) 34 (b) 56 (c) 28 (d) 63

x=3+√81x=13+√8=1(3−√8)(3+√8)(3−√8)=3−√89−8=3−√8 x+1x=3+√8+3−√8=6 (x+1x)2=36x2+1x2+2=36x2+1x2=34 Hence, the correct answer is option (a)

If $x = 3 + \sqrt{8}$ then $(x^{2} + \frac{1}{x^{2}})$ = ?

(a) 34 (b) 56 (c) 28 (d) 63