Question

If x = root3+root2/root3-root2 and y =root3-root2/root3+root2 then find x square+ y square

Answer 1

Answer:

98

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