Question

if x is equal to under root 3 + under root 2 upon under root 3 minus under root 2 and Y is equal to under root 3 minus under root 2 upon under root 3 + under root 2 then find the value of x square+ Y square + x y

Answer 1

hey!
#ur Ans

Given that

X = √3+√2/√3-√2

rationalise the denominator

X = (√3+√2/√3-√2) × (√3+√2/√3+√2)

X = (√3+√2)^2 / (√3^2 -(√2)^2

X = 3+2 +2√6/3-2

X = 5+2√6

then

y = √3-√2/√3+√2

rationalise the denominator

y = 5 -2√6

Now,

$(x + y {)}^{2} = {x }^{2} + {y}^{2} + 2xy \\ \\ put \: the \: valu e \: of \: x \: and \: y \\ \\ (5 + 2 \sqrt{6} + 5 - 2 \sqrt{6} {)}^{2} = {x}^{2} + {y}^{2} + 2xy \\ \\ (10 {)}^{2} = {x}^{2} + {y}^{2} + 2xy \\ \\ x { }^{2} + {y}^{2} + 2xy = 100 \: ans$
✌:-)☺