Question

√5-1/√5+1+/√5+1/√5-1=a+b√5​

Answer 1

Answer:

Step-by-step explanation:

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Plz do rationalisation of  and  separately .

e.g.,  ×  

=  

= (5 + 1 + 2√5)/(5 - 1)

= (6 + 2√5)/4

= (3 + √5)/2

similarly,  ×  

=  

= (5 + 1 - 2√5)/(5 - 1)

= (3 - √5)/2

Now, (3 + √5)/2 + (3 - √5)/2 = a + b√5

(3 + √5 + 3 - √5)/2 = a + b√5

3 = a + b√5

3 + 0.√5 = a + b√5

Compare both sides,

a = 3 and b = 0

Answer 2

Answer:

If a = (√5 + 1) / (√5 - 1) and b = (√5 - 1) / ( √5 + 1) then the value of (a2 + ab + b2) / (a2 - ab + b2) is ?

3/4

4/3

3/5

5/3

Correct Option: B

a = [(√5 + 1) / (√5-1)] x [(√5 + 1) / (√5 + 1)]

= (√5 + 1)2 / (5 - 1)

= (5 + 1 + 2 √5) / 4

= (3 + √5) / 2

b = [(√5 - 1) / (√5 + 1)] x [(√5 - 1 ) / (√5 -1)]

= (√5 - 1 )2 / (5 - 1)

= (5 + 1 - 2√5) / 4

= (3 - √5) / 2

Now a2 + b2 = [(3 + √5)2 + (3 - √5)2] / 4

= [2 x (9 + 5 )] / 4

= 7

ab = 1

∴ (a2 + ab + b2) / (a2 - ab + b2)

= (7 + 1) / (7 - 1)

= 8/6

= 4 / 3 ok follow me ✌️ samile ✌