Loading [MathJax]/jax/output/SVG/config.js
 
+0  
 
0
1113
1
avatar+1836 

Use the Binomial Theorem to write $(3+\sqrt{5})^4$ in the form $a + b\sqrt{5}$ for some positive integers $a$ and $b$.

 May 7, 2015

Best Answer 

 #1
avatar+130466 
+10

(3 + √5)^4 =

3^4  + 4*(3)^3(√5) + 6(3)^2*5  + 4*(3)(√5)^3  + (√5)^4 =

81 + 108√5 + 270 + 12*5√5  + 25 =

81 + 108√5 + 270 + 60√5 + 25 =

376 + 168√5

 

Not too much to that, huh ???

 

  

 May 7, 2015
 #1
avatar+130466 
+10
Best Answer

(3 + √5)^4 =

3^4  + 4*(3)^3(√5) + 6(3)^2*5  + 4*(3)(√5)^3  + (√5)^4 =

81 + 108√5 + 270 + 12*5√5  + 25 =

81 + 108√5 + 270 + 60√5 + 25 =

376 + 168√5

 

Not too much to that, huh ???

 

  

CPhill May 7, 2015

2 Online Users

avatar