Question

if x=9-4√5,find the value of x square -1/x square​

Answer 1

STEP BY STEP EXPLANATION...

$x = 9 - 4 \sqrt{5} \\ to \: find \: \\ - 1 \div x {}^{2} \\ x {}^{2} = (9 - 4 \sqrt{5} ) { }^{2} \\ x {}^{2} = 81 + 80 - 72 \sqrt{5} \\ x {}^{2} = 161 - 72 \sqrt{5} \\ now \\ ( - 1) \div 161 - 72 \sqrt{5} \\( ( - 1) \times 161 + 72 \sqrt{5}) \div (161 - 72 \sqrt{5} ) \times (161 + 72 ) \\ ( - 161 - 72 \sqrt{5} \div (161 {}^{2} - (72 \sqrt{5}) {}^{2} ) \\ (- 161 - 72 \sqrt{5} ) \div (25921 - 25920) \\ - 161 - 72 \sqrt{5} \div 1 \\ = - 161 - 72 \sqrt{5}$

ANS= - 161 - 72 ROOT 5

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