Maths · General term and middle term and simple applications
Evaluate ^{\mathbf{6}}+(\sqrt{\mathbf{3}}+\sqrt{\mathbf{2}})^{\mathbf{6}} \)
Evaluate \( (\sqrt{\mathbf{3}}-\sqrt{\mathbf{2}})^{\mathbf{6}}+(\sqrt{\mathbf{3}}+\sqrt{\mathbf{2}})^{\mathbf{6}} \)
- A. 678
- B. 950
- C. 970 \)
- D. 670
Step-by-step solution
Using binomial theorem: (√3 - √2)^6 + (√3 + √2)^6 = 2 * sum_{k even} C(6,k) (√3)^{6-k} (√2)^k. Compute: k=0: 1*(3^3)=27; k=2: 15*(3^2)*2=270; k=4: 15*3*(2^2)=180; k=6: 1*(2^3)=8. Sum = 27+270+180+8=485; times 2 = 970.
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