Question

if a=3+√5/2 then find the values a²+1/a²

Answer 1

Answer:

6.9998540 or 7(approx)

Step by step explanation:

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

${ a}^{2} = {(3 + \sqrt{5}) }^{2} \div {2 }^{2} \\ {a}^{2} = ( {3}^{2} + ( { \sqrt{5} ) }^{2} + 2 \times 3 \times \sqrt{5)} \div 4 \\ {a }^{2} = (9 + 5 + 6 \sqrt{5)} \div 4 \\ {a}^{2} = (14 + 6 \sqrt{5} ) \div 4 \\ {a}^{2} = (14 + 6 \times 2.236) \div 4 \\ {a }^{2} = (14 + 13.416) \div 4 \\ {a}^{2} = 27.416 \div 4 \\ {a}^{2} = 6.854$

Now,

${a}^{2} + 1 \div {a}^{2}$

=>6.854+1/6.854

Taking L.C.M as 6.854 we get

=>(6.854*6.854+1)/6.854

=>(46.977+1)6.854

=>47.977/6.854

=>6.9998540

=>which is approximately equal to 7.

If understood please mark it as brainliest.