If x-3-8 then x 2-1 x 2- -a 34b 56c 28d 63

Given: nbsp;x=3+8 1x=13+8=13+8 #215;3 83 8=3 89 8=3 81=3 8 x+1x=3+8+3 8=6 x+1x2=x2+1x2+2 #215;x #215;1x=x2+1x2+2 #8658;62=x2+1x2+2 #8658;36=x2+1x2+2 ...

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Byju's Answer

Standard IX

Mathematics

Polynomials

If x=3+8 then...

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

Given: $x = 3 + \sqrt{8}$
$\frac{1}{x} = \frac{1}{3 + \sqrt{8}} = \frac{1}{3 + \sqrt{8}} \times \frac{3 - \sqrt{8}}{3 - \sqrt{8}} = \frac{3 - \sqrt{8}}{9 - 8} = \frac{3 - \sqrt{8}}{1} = 3 - \sqrt{8}$
$x + \frac{1}{x} = (3 + \sqrt{8}) + (3 - \sqrt{8}) = 6$
${(x + \frac{1}{x})}^{2} = x^{2} + \frac{1}{x^{2}} + 2 \times x \times \frac{1}{x} = x^{2} + \frac{1}{x^{2}} + 2 \Rightarrow 6^{2} = x^{2} + \frac{1}{x^{2}} + 2 \Rightarrow 36 = x^{2} + \frac{1}{x^{2}} + 2 \Rightarrow x^{2} + \frac{1}{x^{2}} = 36 - 2 = 34$
Hence, the correct answer is option (a).

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Similar questions

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

x = (3 + \sqrt{8})

, find the value of

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

If $x = 3 + \sqrt{8}$

then $x^{4} + \frac{1}{x^{4}} =$ ______

Solve

x = 3 + \sqrt{8}

, find

x^{2} - \frac{1}{x^{2}}

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

Given: x=3+8 1x=13+8=13+8×3-83-8=3-89-8=3-81=3-8 x+1x=3+8+3-8=6 x+1x2=x2+1x2+2×x×1x=x2+1x2+2⇒62=x2+1x2+2⇒36=x2+1x2+2⇒x2+1x2=36-2=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