If X-2 -3-2-2 -3-2 andY-3-2-2 - 3-2Find X2-Y2-X Y-X2-Y2-X Y

The correct option is C 195/193 if X = √(3)+2/√(3) 2 and Y = √(3) 2/√(3)+2 X+Y = √(3)+2/√(3) 2 +√(3) 2/√(3)+2 X+Y = (√(3)+2)^2+(√(3) 2)^2/(√(3))^2 2^2 X+Y= 3+ ...

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Byju's Answer

Standard VII

Mathematics

(a + b)^2 Expansion and Visualisation

if X=2 √3+2/2...

Question

if $X = \frac{\sqrt[2]{3} + 2}{\sqrt[2]{3} - 2}$ and

$Y = \frac{\sqrt[2]{3} - 2}{\sqrt[2]{3} + 2}$

Find $\frac{X^{2} + Y^{2} - X Y}{X^{2} + Y^{2} + X Y}$

$\frac{195}{193}$

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$\frac{191}{196}$

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$\frac{196}{191}$

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$\frac{193}{195}$

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Solution

The correct option is A
$\frac{195}{193}$

if $X = \frac{\sqrt[2]{3} + 2}{\sqrt[2]{3} - 2}$ and

$Y = \frac{\sqrt[2]{3} - 2}{\sqrt[2]{3} + 2}$

$X + Y = \frac{\sqrt[2]{3} + 2}{\sqrt[2]{3} - 2} + \frac{\sqrt[2]{3} - 2}{\sqrt[2]{3} + 2}$
$X + Y = \frac{(\sqrt[2]{3} + 2)^{2} + (\sqrt[2]{3} - 2)^{2}}{(\sqrt[2]{3})^{2} - 2^{2}}$
$X + Y = \frac{3 + 4 + 4 \sqrt[2]{3} + 3 + 4 - 4 \sqrt[2]{3}}{3 - 2}$
$X + Y = 14.................... e q (i)$

$X - Y = \frac{\sqrt[2]{3} + 2}{\sqrt[2]{3} - 2} - \frac{\sqrt[2]{3} - 2}{\sqrt[2]{3} + 2}$
$X - Y = \frac{(\sqrt[2]{3} + 2)^{2} - (\sqrt[2]{3} - 2)^{2}}{(\sqrt[2]{3})^{2} - 2^{2}}$
$X - Y = \frac{3 + 4 + 4 \sqrt[2]{3} - 3 - 4 + 4 \sqrt[2]{3}}{3 - 2}$
$X - Y = 8 \sqrt[2]{3} . . . . . . . . . . . . . . . . . . . e q (i i)$

$X Y = (\frac{\sqrt[2]{3} + 2}{\sqrt[2]{3} - 2}) (\frac{\sqrt[2]{3} - 2}{\sqrt[2]{3} + 2})$

$X Y = \frac{(\sqrt[2]{3})^{2} - 2^{2}}{(\sqrt[2]{3})^{2} - 2^{2}})$
$X Y = 1......................... e q (i i i)$

Now $\frac{X^{2} + Y^{2} + X Y}{X^{2} + Y^{2} - X Y}$ can be written as

$\frac{(X + Y)^{2} - X Y}{(X - Y)^{2} + X Y}$

Substituting the value we get
$\frac{14^{2} - 1}{(8 \sqrt[2]{3})^{2} - 1} = \frac{196 - 1}{192 + 1} = \frac{195}{193}$

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Similar questions

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\frac{\sqrt{3} - \sqrt{2}}{\sqrt{3} + \sqrt{2}},

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$Y = \frac{\sqrt[2]{3} - 2}{\sqrt[2]{3} + 2}$

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