Question

is (5+root3)^2 +(5-root3)^2 a rational number justify
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Answer 1

$Given \: ( 5 + \sqrt{3})^{2} + ( 5 - \sqrt{3})^{2}$

/* By algebraic identities */

$\boxed {\pink { (a+b)^{2} + (a-b)^{2} = 2(a^{2} + b^{2} ) }}$

$= [ 2( 5^{2} + ( \sqrt{3})^{2} ]$

$= 2( 25 + 3 )$

$= 2 \times 28$

$= 56\: \blue{ ( Rational \: number )}$

Therefore.,

$\red{ ( 5 + \sqrt{3})^{2} + ( 5 - \sqrt{3})^{2}}$

$\green {= 56}\: \blue{ ( Rational \: number )}$

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