Question

one over root 19 minus root 360 - 1 over root 21 - root 440 + 2 over root 20 + root 396​

Answer 1

Answer:

ask from doubt nut

Step-by-step explanation:

Answer 2

Step-by-step explanation:

Given:-

1/√[19 - √(360)] - 1/√[21 - √(440)] + 2/√[20 + √(396)] = ?

To find:-

Simplify.

Solution:-

We have,

1/√[19 - √(360)] - 1/√[21 - √(440)] + 2/√[20 + √(396)]

= 1/√[19 - 2√(90)] - 1/√[21 - 2√(110)] + 2/√[20 + 2√(99)]

= 1/√[(√10)^2 + √(9)^2 - 2√(10)√(9)] - 1/√[(10)^2 + (√11)^2 - 2√(10)√(11)] + 2/√[(11)^2 + (√9)^2 - 2√(11)√(9)]

= 1/√[{√(10) - √(9)}]^2 - 1/√[{√(11) - √(10)}]^2 + 2/√[{√(11) + √(9)}]^2

= 1/[√(10) - √(9)] - 1/[√(11) - √(10)] + 2/[√(11) - √(9)]

= [1/{√(10) - √(9)} × {√(10) + √(9)}/{√(10) + √(9)] - [1/{√(11) - √(10)} × {√(11) + √(10)}/{√(11) + √(10)] + [2/{√(11) + √(9)} × {√(11) - √(9)}/{√(11) - √(9)}]

= [{√(10) + √(9)}/(10 - 9)] - [{√(11) + √(10)}/(11 - 10)] + [2{√(11) - √(9)}/(11 - 9)]

= [{√(10) + √(9)}/1] - [{√(11) + √(10)}/1] + [2{√(11) - √(9)}/2]

= √(10) + √(9) - √(11) - √(10) + [2{√(11) - √(9)}/2]

= √(10) + √(9) - √(11) - √(10) + √(11) - √(9)

= 0 Ans.