Asked by Aasher
if a=root 3 - root 2 ÷ root 3 + root 2 of b = root 3 + root 2 ÷ root 3 - root 2 find a square + b square = 5ab
Answers
Answered by
Steve
a = (√3-√2)/(√3+√2)
b = (√3+√2)/(√3-√2)
Clearly ab=1
Doing the squares directly is a bit cumbersome, so let's rationalize the denominators:
a = (√3-√2)^2 = 5-2√6
b = (√3+√2)^2 = 5+2√6
Now we can take
a^2 = 49-20√6
b^2 = 49+20√6
a^2+b^2 = 98
Not sure that 98 = 5*1
b = (√3+√2)/(√3-√2)
Clearly ab=1
Doing the squares directly is a bit cumbersome, so let's rationalize the denominators:
a = (√3-√2)^2 = 5-2√6
b = (√3+√2)^2 = 5+2√6
Now we can take
a^2 = 49-20√6
b^2 = 49+20√6
a^2+b^2 = 98
Not sure that 98 = 5*1
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