Question

√√5+2 +√√5-2/√√5+1 please solve it​

Answer 1

•●○ ANSWER ○●•

Given,

P = {√(√5 + 2) + √(√5 -2)}/√(√5 + 1) - {√3 - 2√2}

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

Again,

√[3 – 2√2] = √[2 + 1 – 2√2]

                         = √[(√2 – 1)2 ]

                         = √2 – 1

Now,

P = { √[√5 + 2] +√[√5 – 2] }

√[√5 + 1] – √[3 – 2√2]

=> P = √2 – (√2 – 1)

=> P = √2 – √2 + 1

=> P = 1

So, the value of P is 1