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Answers
Answer:
16.0
Step-by-step explanation:
the square root of 3 and the 3 on the denominator plus the square root of 2 and the 2 on the denominaror is 4, now repeat it for letter y then add the 2 answers, 4.0 will come out, if we then do 4.0 x 4.0 (because of the 4.0 squared thingy) we will get 16.0
so the answer is 16.0
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x = ( √3 + √2 ) / ( √3 - √2 )
Rationalizing
[(√3 + √2)(√3 + √2) ] / [ (√3 - √2) (√3 + √2) ]
Numerator is ( a+b )² = a² + b² + 2ab
Denominator is ( a-b ) ( a+b) = a² - b²
Therefore,
[ (√3)² + (√2)² + 2 (√3)(√2) ] / [ (√3)² - (√2)² ]
= ( 3+2 + 2×√6 ) / 3-2
= 5 + 2√6 / 1 = x
y = ( √3 - √2 ) / (√3+√2 )
Rationalizing
[ ( √3 - √2 ) (√3 - √2 ) ] / (√3+√2 ) (√3 - √2 ) ]
Numerator is ( a-b )² = a² + b² - 2ab
Denominator is ( a-b ) ( a+b) = a² - b²
Therefore,
[ (√3)² + (√2)² - 2 (√3)(√2) ] / [ (√3)² - (√2)² ]
= ( 3+2 - 2×√6 ) / 3-2
= 5 - 2√6 / 1 = y
485 + 198√6 = (5+2√6 )³
485 - 198√6 = (5-2√6 )³
x³ + y³ = 485 + 198√6 + 485 - 198√6
x ³ + y³ = 970