Question

if a=√5+2 , then a^2+1/a^2 =
please solve step by step ​

Answer 1

Answer:

Solution :

given,a=3+5–√2

1a=23+5–√=23+5–√×3−5–√3−5–√

[multiplying numerator and denominator by 3−5–√)

6−25–√32−(5–√)2 [using identity,(a−b)(a+b)=a2−b2]

6−25–√9−5=6−25–√4

1a=2(3−5–√)4=3−5–√2

a2+1a2a2+1a2+2−2=(a+1a)2−2 [adding and subtarcting2]

(3+5–√2+3−5–√2)2−2 [from Eqs. (i)and (ii)]

(62)2−2=(3)2−2=9−2=7

Answer 2

here u can do it in 2 ways

1. either u can find the values of a and 1/a and put them to find the ans
2. or u can apply (a+1/a)² = [√5+2 + 1/(√5 + 2)]

ans in attachment u