Binomial expansion question hard surds core 1 Watch

wednesday_adams
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#1
Report Thread starter 4 years ago
#1
This is a core 1 binomial expansion question for mei:

given that (√3-√2)^5 = a√3 - b√2 evaluate a and b

please help
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wednesday_adams
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#2
Report Thread starter 4 years ago
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someone told me a is 89 and b is -109 but i have no clue how they got there??? could anyone help me to figure out how to solve??
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NewKidToTheBlock
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you can use Pascal's triangle to help with this:
so because it's to the power of 5 you use the numbers ~ 1, 5, 10, 10, 5, 1
so then you create the equation:

1(√ 3)^0(-√ 2)^5 + 5(√ 3)^1(-√ 2)^4 + 10(√ 3)^2(-√ 2)^3 + 10(√ 3)^3(-√ 2)^2 + 5(√ 3)^4(-√ 2)^1 +1(√ 3)^5(-√ 2)^0
= -5.657 + 34.64 -60√ 2 +60√ 3 -63.64 + 15.59

then you look for the 2 components that have √ 2 and √ 3 ; they are A&b,
however i got a= -60 & b= 60 not 89 and -109

this is what i was taught so don't take my word for it
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