Question

if x = √3 - √2/√3 + √2 and y = √3 + √2/√3 - √2 find x² + y² +xy

Answer 1

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Step-by-step explanation:

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x=√3-√2/√3+√2=(√3-√2)(√3-√2)/(√3+√2)(√3-√2)=(√3-√2)²/(√3)²-(√2)²

 =(√3-√2)²/3-2=(√3-√2)²=(3-2√6+2)=(5-2√6)

y=√3+√2/√3-√2=(√3+√2)(√3+√2)/(√3-√2)(√3+√2)=(√3+√2)²/(√3)²-(√2)²

 =(√3+√2)²/3-2=(√3+√2)²=(3+2√6+2)=(5+2√6)

xy=(√3-√2)²×(√3+√2)²={(√3)²-2×√3×√2+(√2)²}{(√3)²+2×√3×√2+(√2)²}

  =(3-2√6+2)(3+2√6+2)=(5-2√6)(5+2√6)=5²-(2√6)²=25-24=1

∴x²+y²+xy=​(5-2√6)²+(5+2√6)²+1

               =5²-2×5×2√6+(2√6)²+5²+2×5×2√6+(2√6)²+1

               =25+24+25+24+1=99