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Yogita Ingle 6 years, 5 months ago
first 10 natural number=1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 = 55
Mean = 55/10 = 5.5
now, 5th and 6th term as the total number is even .
Median = 5+6/2 = 11/ 2 = 5.5
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Sia ? 6 years, 5 months ago
It is given that,
x = 3 + {tex}\sqrt{8}{/tex}
Now, {tex}\frac{1}{x}{/tex} = {tex}\frac{1}{3+\sqrt{8}}{/tex} = {tex}\frac{1}{3+\sqrt{8}} \times \frac{3-\sqrt{8}}{3-\sqrt{8}}{/tex} ( rationalising the expression)
= {tex}\frac{3-\sqrt{8}}{(3)^{2}-(\sqrt{8})^{2}}{/tex}
= {tex}\frac{3-\sqrt{8}}{9-8}{/tex} = 3 - {tex}\sqrt{8}{/tex}
{tex}\Rightarrow{/tex} {tex}\frac{1}{x}{/tex} = 3 - {tex}\sqrt{8}{/tex}
We know that, (x + {tex}\frac{1}{x}{/tex})2 = x2 + {tex}\frac{1}{x^2}{/tex} + 2 {tex}\times{/tex} x {tex}\times{/tex} {tex}\frac{1}{x}{/tex}
{tex}\Rightarrow{/tex} (3 + {tex}\sqrt{8}{/tex} + 3 - {tex}\sqrt{8}{/tex})2 = x2 + {tex}\frac{1}{x^2}{/tex} + 2
{tex}\Rightarrow{/tex} (6)2 = x2 + {tex}\frac{1}{x^2}{/tex} + 2
{tex}\Rightarrow{/tex} 36 = x2 + {tex}\frac{1}{x^2}{/tex} + 2
{tex}\Rightarrow{/tex} x2 + {tex}\frac{1}{x^2}{/tex} = 36 - 2 = 34
Hence, x2 + {tex}\frac{1}{x^2}{/tex} = 34
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My Cbse Guide My Cbse Guide 6 years, 5 months ago
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