If N = [{√(√5+2) + √(√5-2)}/√(√5+1)] - √(√5+1), then find the value of N. (last answer that you gave was wrong).
Given, P = {√(√5 + 2) + √(√5 -2)}/√(√5 + 1) - {√(√5 + 1)}
Now, {√[√5 + 2] +√[√5 – 2]}/√[√5 + 1]
= { √[√5 + 2] + √[√5 – 2] } √[√5 – 1] / (√[√5 + 1] √[√5 – 1])
= { √[(√5 + 2)(√5 – 1)] + √[(√5 – 2)(√5 – 1)] } / √[(√5 + 1)(√5 – 1)]
= { √[5 – √5 + 2√5 – 2] + √[5 – √5 – 2√5 + 2] } / √[5 – 1]
= { √[3 + √5] + √[7 – 3√5] } / 2
= { √[(6 + 2√5)/2] + √[(14 – 6√5)/2] } / 2
= { √[(1 + 5 + 2√5)/2] + √[(9 + 5 – 6√5)/2] } / 2
= { √[(1 + √5)2 /2] + √[(3 – √5)2 /2] } / 2
= { (1 + √5)/√2 + (3 – √5)/√2 } / 2
= { (1 + √5) + (3 – √5) } / (2√2)
= 4 / (2√2)
= √2
So from first equation
= √2 - √(√5 + 1)]