If x-y-3-5-32-3- then the values of x and yrespectively are

X+y√(3)=5 √(3)2+√(3)×2 √(3)2 √(3) =10 5√(3) 2√(3)+3(2)^2 (√(3))^2 =13 7√(3)4 3 ⇒ x+y √(3)=13 7√(3) Comparing both sides, we get x=13, y= 7 So, option a is ...

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Byju's Answer

Standard IX

Mathematics

Rationalisation

If x+y√3=5-√3...

Question

$If x + y \sqrt{3} = \frac{5 - \sqrt{3}}{2 + \sqrt{3}}, then the values of x and y respectively are$

13 and -7

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-13 and -7

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13 and 7

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13 and -13

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Solution

The correct option is A
13 and -7
$x + y \sqrt{3} = \frac{5 - \sqrt{3}}{2 + \sqrt{3}} \times \frac{2 - \sqrt{3}}{2 - \sqrt{3}} = \frac{10 - 5 \sqrt{3} - 2 \sqrt{3} + 3}{(2)^{2} - (\sqrt{3})^{2}} = \frac{13 - 7 \sqrt{3}}{4 - 3} \Rightarrow x + y \sqrt{3} = 13 - 7 \sqrt{3} Comparing both sides, we get x = 13, y = - 7$

So, option a is correct.

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If x+y√3=5−√32+√3,then the values of x and yrespectively are

The correct option is A 13 and -7x+y√3=5−√32+√3×2−√32−√3=10−5√3−2√3+3(2)2−(√3)2=13−7√34−3⇒x+y√3=13−7√3Comparing both sides, we getx=13, y=−7 So, option a is correct.

$If x + y \sqrt{3} = \frac{5 - \sqrt{3}}{2 + \sqrt{3}}, then the values of x and y respectively are$