If x -6-35- then x 2-1- x 2-A- 140B- 120C- 144D- 142

The correct option is D 142 x=6 √(35) 1/x = 1/6 √(35)×6+√(35)/6+√(35) =6+√(35)/(6)^2 (√(35))^2 =6+√(35)/36 35 =6+√(35) Therefore, x+1/x = 6 √(35) + 6 +√(35) ...

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Byju's Answer

Standard IX

Mathematics

Division of Surds by Rationalisation

If x =6-√35, ...

Question

If $x = 6 - \sqrt{35}$ , then $x^{2} + \frac{1}{x^{2}} =$ ___

144

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142

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140

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120

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Solution

The correct option is B
142

$x = 6 - \sqrt{35}$

$\frac{1}{x} = \frac{1}{6 - \sqrt{35}} \times \frac{6 + \sqrt{35}}{6 + \sqrt{35}}$

$= \frac{6 + \sqrt{35}}{(6)^{2} - (\sqrt{35})^{2}}$

$= \frac{6 + \sqrt{35}}{36 - 35}$

$= 6 + \sqrt{35}$

Therefore, $x + \frac{1}{x} = 6 - \sqrt{35} + 6 + \sqrt{35}$

$= 12$

We know, ${(x + \frac{1}{x})}^{2} = x^{2} + 2 + \frac{1}{x^{2}}$

$(12)^{2} = x^{2} + \frac{1}{x^{2}} + 2$

$∴ x^{2} + \frac{1}{x^{2}} = 144 - 2$

$= 142$

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If x=6−√35, then x2+1x2= ___

The correct option is B 142 x=6−√35 1x=16−√35×6+√356+√35 =6+√35(6)2−(√35)2 =6+√3536−35 =6+√35 Therefore, x+1x=6−√35+6+√35 =12 We know, (x+1x)2=x2+2+1x2 (12)2=x2+1x2+2 ∴x2+1x2=144−2 =142

If $x = 6 - \sqrt{35}$ , then $x^{2} + \frac{1}{x^{2}} =$ ___