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Evaluate the following: \ (sqrt(3)+1)^5-...

Evaluate the following: `\ (sqrt(3)+1)^5-(sqrt(3)-1)^5`

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To evaluate the expression \((\sqrt{3}+1)^5 - (\sqrt{3}-1)^5\), we can use the Binomial Theorem. ### Step-by-Step Solution: 1. **Identify the terms for the Binomial Expansion**: We can express \((\sqrt{3}+1)^5\) and \((\sqrt{3}-1)^5\) using the Binomial Theorem: \[ (x + a)^n = \sum_{k=0}^{n} \binom{n}{k} x^{n-k} a^k ...
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RD SHARMA-BINOMIAL THEOREM-Solved Examples And Exercises
  1. Evaluate the following: \ (3+sqrt(2))^5-(3-sqrt(2))^5

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  2. Evaluate the following: \ (1+2sqrt(x))^5+(1-2sqrt(x))^5

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  3. Evaluate the following: \ (sqrt(3)+1)^5-(sqrt(3)-1)^5

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  4. Evaluate the following: \ (sqrt(3)+sqrt(2))^6-(sqrt(3)-sqrt(2))^6

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  5. Evaluate the following: \ {a^2+sqrt(a^2-1)}^4+{a^2-sqrt(a^2-1)}^4

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  6. Evaluate the following: \ (x+sqrt(x^2-1))^6+(x-sqrt(x^2-1))^6

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  7. Evaluate the following: \ (sqrt(2)+1)^6+(sqrt(2)-1)^6

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  8. Evaluate the following: (2+sqrt(3))^7+(2-sqrt(3))^7

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  9. Evaluate the following: \ (0. 99)^5+(1. 01)^5

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  10. Find (a+b)^4-(a-b)^4dot Hence evaluate (sqrt(3)+sqrt(2))^4-(sqrt(3)-sq...

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  11. Find (x+1)^6+(x-1)^6. Hence evaluate (sqrt(2)+1)^6+(sqrt(2)-1)^6.

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  12. Using binomial theorem evaluate each of the following: (96)^3

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  13. Using binomial theorem evaluate each of the following: (102)^5

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  14. Using binomial theorem evaluate each of the following: (101)^4

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  15. Using binomial theorem evaluate each of the following: (98)^5

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  16. Using binomial theorem indicate which is larger (1. 1)^(10000)or\ 1000...

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  17. Write the general term in the expansion of (x^2-y)^6dot

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  18. Find the 10th term in the binomial expansion of (2x^2+1/x)^(12)dot

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  19. Find the constant term in the expansion of ((4x^2)/3+3/(2x))^9.

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  20. Find 13th term in the expansion of (9x-1/(3sqrtx))^(18),\ x!=0.

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