if a is 5 + 2 \sqrt{6} \: then \: find \: the \: value \: of \: \: a + \frac{1}{a}

Question

if a is
5 + 2 \sqrt{6}  \: then \: find \: the \: value \: of \:  \:  a +  \frac{1}{a}

in progress 0
Adalynn 2 weeks 2021-09-07T12:39:16+00:00 1 Answer 0 views 0

Answers ( )

    0
    2021-09-07T12:40:57+00:00

    Step-by-step explanation:

    solution:

    a = 5 + 2 \sqrt{6}

    we have find

    a +  \frac{1}{a}  \\

    so value of a is given then put the value of a

    5 + 2 \sqrt{6}  +  \frac{1}{5 + 2 \sqrt{6} }  \\

    now take a lcm

     \frac{(5 + 2 \sqrt{6} )(5 + 2 \sqrt{6}) + 1 }{5 + 2 \sqrt{6} }  \\  \frac{(5 + 2 \sqrt{6} ) { }^{2}  + 1}{5 + 2 \sqrt{6} }  \\  \frac{5 {}^{2} + (2 \sqrt{6} ) {}^{2}   + 5 \times 2 \times 2 \sqrt{6}  + 1}{5 + 2 \sqrt{6} }  \\  \frac{25 + 24 + 20 \sqrt{6}  + 1}{5 + 2 \sqrt{6} }  \\  \frac{50 + 20 \sqrt{6} }{5 + 2 \sqrt{6} }  \\

    take 10 common from nominator

     \frac{10 (5 + 2 \sqrt{6} )}{5 + 2 \sqrt{6} }  \\ 5 + 2 \sqrt{6}  \: is \: same \: so \: it \: cancle \: out \\ \implies10

    ANSWER: 10

Leave an answer

Browse
Browse

18:9+8+9*3-7:3-1*13 = ? ( )