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fenix001 [56]
3 years ago
14

What is the answer to this question?(3+√5)^2

Mathematics
2 answers:
Keith_Richards [23]3 years ago
6 0
14 + 6√5 because foil method

(3+√5)^2 = (3+√5)(3+√5)

3(3) = 9
3(√5) = 3√5
√5(3) = 3√5
√5(√5) = 5

9 + 3√5 + 3√5 + 5
= 14 + 6√5
slavikrds [6]3 years ago
4 0

Answer:

the answer to this is

14 + 6√5

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1/5 is less then 5/8
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WINSTONCH [101]


In general the binomial expansion is


(a+b)^n = {n \choose 0} a^0 b^n + {n \choose 1} a^1 b^{n-1} + {n \choose 2} a^2 b^{n-2} + ... + {n \choose n} a^n b^0


So in our case, because we want ascending powers of x we'll write,


(-3x + 1)^{11} =  {11 \choose 0} (-3x)^0 1^{11} + {11 \choose 1} (-3x)^{1} 1^{10} + {11 \choose 2} (-3x)^{2} 1^9  + {11 \choose 3 } (-3x)^3 1^8 + ...


We need to calculate the binomial coefficients:


{11 \choose 0}  = 1


{11 \choose 1}  = 11


{11 \choose 2}  = \dfrac{11 \times 10}{2} = 55


{11 \choose 3}  = \dfrac{11 \times 10 \times 9}{3 \times 2} = 165


(-3x+1)^{11} =  1 (-3x)^0 1^{11}  + 11(-3x)^{1} 1^{10}  + 55 (-3x)^2 1^{9}  + 165 (-3x)^3 1^8 + ...


(1-3x)^{11} =  1 -33 x + 495 3x^2 - 4455 x^3+ ...



6 0
3 years ago
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