Question

simplify 1 by root 3 + root 2 minus 2 by root 5 minus root 3 minus 3 by root 2 minus root 5​

Answer 1

Answer:

2/(√5 +√3) + 1/(√3 +√2) - 3/(√5 +√2) = 0

Solution :-

We need to find the value of ;

2/(√5 + √3) + 1/(√3 + √2) - 3/(√5 + √2)

Now ,

• 2/(√5 + √3)

= 2(√5 - √3) / (√5 + √3)•(√5 - √3)

= 2(√5 - √3) / [ (√5)² - (√3)² ]

= 2(√5 - √3) / (5 - 3)

= 2(√5 - √3) / 2

= √5 - √3

• 1/(√3 + √2)

= (√3 - √2) / (√3 + √2)•(√3 - √2)

= (√3 - √2) / [ (√3)² - (√2)² ]

= (√3 - √2) / (3 - 2)

= (√3 - √2) / 1

= √3 - √2

• 3/(√5 + √2)

= 3(√5 - √2) / (√5 + √2)•(√5 - √2)

= 3(√5 - √2) / [ (√5)² - (√2)² ]

= 3(√5 - √2) / (5 - 2)

= 3(√5 - √2) / 3

= √5 - √2

Now ,

2/(√5 + √3) + 1/(√3 + √2) - 3/(√5 + √2)

= (√5 - √3) + (√3 - √2) - (√5 - √2)

= √5 - √3 + √3 - √2 - √5 + √2

= 0

Hence ,

2/(√5 +√3) + 1/(√3 +√2) - 3/(√5 +√2) = 0