Question

Simplify ( 2root 5 + 3 root2)² + (2 root 5 - 3 root 2)²​

Answer 1

Solution

a² + b² = (a + b) ² - 2ab

a = $2\sqrt{5}\: + \: 3\sqrt{2}$

b = $2\sqrt{5}\: - \: 3\sqrt{2}$

Now,

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

$\implies (2\sqrt{5}\:+\:2\sqrt{5})^{2}\: - \: 2[(2\sqrt{5})^{2}\:-\: (3\sqrt{2})^{2}]$

$\implies (4\sqrt{5})^{2}\: - \: 2[20\: - \: 18]$

$\implies 80\: - \: 2(2)$

$\implies 80\: - \: 4$

$\implies 76$

Answer 2

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