The correct option is C 14(2+√(3))^2=2^2+√(3)^2+2× 2×√(3) =4+3+4√(3) =7+4√(3) ... (1) (2 √(3))^2=2^2+√(3)^2 2× 2×√(3) =4+3 4√(3) =7 4√(3) ... (2) Adding equatio ...

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Conjugate Pair

(2+√(3))^2+(2...

Question

$(2 + \sqrt{3})^{2} + (2 - \sqrt{3})^{2} =$

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Solution

The correct option is C 14
$(2 + \sqrt{3})^{2} = 2^{2} + {\sqrt{3}}^{2} + 2 \times 2 \times \sqrt{3}$
$= 4 + 3 + 4 \sqrt{3}$
$= 7 + 4 \sqrt{3}$ ... (1)
$(2 - \sqrt{3})^{2} = 2^{2} + {\sqrt{3}}^{2} - 2 \times 2 \times \sqrt{3}$
$= 4 + 3 - 4 \sqrt{3}$
$= 7 - 4 \sqrt{3}$ ... (2)
Adding equation (1) and (2):
$7 + 4 \sqrt{3} + 7 - 4 \sqrt{3} = 14$

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Similar questions

$32 + (22 + 2) = (32 +___) + 2$

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(2 + \sqrt{3})^{2} + (2 - \sqrt{3})^{2} =

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(2+√3)2+(2−√3)2=

The correct option is C 14(2+√3)2=22+√32+2×2×√3 =4+3+4√3 =7+4√3 ... (1) (2−√3)2=22+√32−2×2×√3 =4+3−4√3 =7−4√3 ... (2) Adding equation (1) and (2): 7+4√3+7−4√3=14

$(2 + \sqrt{3})^{2} + (2 - \sqrt{3})^{2} =$