Question

if x=3+2 root 2,find the value of[root x-1 / rooot x]

Answer 1

Hey friend,
Here is the answer you were looking for:
$x = 3 + 2 \sqrt{2} \\ \\ \frac{1}{x} = \frac{1}{3 + 2 \sqrt{2} } \\ \\ on \: rationalizing \: the \: denominator \: we \: get \\ \\ \frac{1}{x} = \frac{1}{3 + 2 \sqrt{2} } \times \frac{3 - 2 \sqrt{2} }{3 - 2 \sqrt{2} } \\ \\ using \: the \: identity \\ (a + b)(a - b) = {a}^{2} - {b}^{2} \\ \\ \frac{1}{x} = \frac{3 - 2 \sqrt{2} }{ {(3)}^{2} - {(2 \sqrt{2}) }^{2} } \\ \\ \frac{1}{x} = \frac{3 - 2 \sqrt{2} }{9 - 8} \\ \\ \frac{1}{x} = 3 - 2 \sqrt{2} \\ \\ x + \frac{1}{x} = (3 + 2 \sqrt{2} ) + (3 - 2 \sqrt{2} ) \\ \\ x + \frac{1}{x} = 3 + 2 \sqrt{2} + 3 - 2 \sqrt{2} \\ \\ x + \frac{1}{x} = 3 + 3 \\ \\ x + \frac{1}{x} = 6$


Hope this helps!!!

@Mahak24

Thanks...
☺☺

Answer 2

Answer:The cubed root of nine thousand, one hundred and ninety-seven ∛9197 = 20.95

Step-by-step explanation: