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CBSE Class 10 Answered

Please solve the question 
question image
Asked by vikasg13.hardware | 22 Jun, 2018, 09:56: PM
answered-by-expert Expert Answer
√n + √(n+1) < 11
 
Subtract √(n+1) from both sides:
√n < 11 - √(n+1) 
 
Square both sides:
n < 121 - 22√(n+1) + n + 1
 
Subtract n from both sides and simplify the right hand side:
0 < 122 - 22√(n+1) 
 
Add 22√(n+1) to both sides:
22√(n+1)  < 122
 
Divide both sides by 22:
√(n+1) < 122/22
 
√(n+1) < 61/11
 
Square both sides:
n+1 < 3721/121 = 30.75
 
Subtract 1 from both sides:
n < 29.75
 
Therefore, positive integers 1-29 should work!
 
We can check this:
√29 + √30 = 10.86
 
If we go to n = 30, it should be greater than 11:
√30 + √31 = 11.05
 
Therefore, your answer is x < 30.
Answered by Arun | 25 Jun, 2018, 02:06: PM

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