If x=root3+root2/root3-root2 and y=root 3-root 2/root3+root 2, find x cube + y cube
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Answer:
here is your answer in detail <3
Step-by-step explanation:
X =(√3+√2)/(√3-√2)
By taking conjugate, we get
X = (√3+√2) (√3+√2) /(√3-√2) (√3+√2)
=(√3+√2)²/(√3²-√2²)
=3+2√6+2 / (3-2) = 5+2√6
Y = (√3-√2)/(√3+√2)
By taking conjugate we get
Y = (√3-√2)²/ (√3+√2)(√3-√2)
= 3-2√6+2/√3²-√2²
= 5-2√6/(3-2) = 5-2√6
X² = (5+2√6)² = 25+20√6+24 = 49+20√6
Y² = (5-2√6)² = 25-20√6+24 = 49-20√6
X²+Y² = 49+20√6+49-20√6
X²+Y² = 98
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