Question

$if \: x = \sqrt{ \frac{5 + \sqrt{6} }{5 - 2 \sqrt{6} } } \: show \: that \: {x}^{2} (x - 10)^{2} = 1$
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Answer 1

Answer:

1 Ans

Step-by-step explanation:

Question:

$if \: x = \sqrt{ \frac{5 + 2 \sqrt{6} }{5 - 2 \sqrt{6} } } \: show \: that \: {x}^{2} (x - 10)^{2} = 1$

Solution:

$x = \sqrt{ \frac{5 + 2 \sqrt{6} }{6} \times \frac{5 + 2 \sqrt{6} }{5 + 2 \sqrt{6} } } = \sqrt{ \frac{(5 + 2 \sqrt{6})^{2} }{ ({5})^{2} - (2 \sqrt{6} )^{2} } } \\ = \frac{5 + 2 \sqrt{6} }{ \sqrt{25 - 24} } = \frac{5 + 2 \sqrt{6} }{1} = 5 + 2 \sqrt{6}$

∴ x²(x-10)² = (5+2√6)²(5+2√6-10)²

$= (5 + 2 \sqrt{6} )^{2} (2 \sqrt{6} - 5) ^{2} \\ = (25 + 24 + 20 \sqrt{6} )(24 + 25 - 20 \sqrt{6} ) \\ = (49 + 20 \sqrt{6} )(49 - 20 \sqrt{6} ) \\ = ( {49})^{2} - (20 \sqrt{6} ) ^{2} \\ = 2401 - 2400 = 1 \: ans.$

Answer 2

ANSWER IN ATTACHMENT FILE