Question

If m=2+√5 then find m^2 + 1/m^2
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Answer 1

Answer:

(2+√5)^2+1/(2+√5)^2

17.944 + 0.0557

17.9997

Answer 2

Answer:

m² = (2+√5)²

m² = 4 + 5 +4√5

m²= 9 +4√5

putting in equation

m²+ 1/m²

9+4√5 + 1/(9+ 4√5)

((9+4√5)² +1)/(9 +4 √5)

( 81 + 80 + 72√5 +1) / (9 + 4√5)

( 162 + 72√5) / (9 + 4√5)

rationalization

18( 9 + 4√5) (9 -4 √5) / (9+ 4√5)(9-4√5)

18(9² -(4√5)²) / 9² -(4√5)²

18 (81 - 80)/ 81 - 80

18 * 1 / 1

18

Hope It May Help You.....