Question

If x(2-√3)=y(2-√3)=1,then find the value of 3x²-5xy-3y²

Answer 1

Answer: -35-20×3^1/2

Step-by-step explanation:

Answer 2

Answer:

Step-by-step explanation:

we know  x(2-√3)=1 and y(2-√3)=1

No we have to find 3x^2-5xy-3y^2.

if x(2-√3)=1 that implies

x= 1/(2-√3)                        (take conjugate)

  = (2+√3)/(2-√3)(2+√3)         (a+b)(a-b) = a^2 - b^2

  =(2+√3)/(4-3)

  =2+√3

avd

y =  1/(2-√3)                        (take conjugate)

  = (2+√3)/(2-√3)(2+√3)         (a+b)(a-b) = a^2 - b^2

  =(2+√3)/(4-3)

  =2+√3

now substitute the the value of x and y in given,

3x^2 and -3y^2 will be cancelled,,so

-5xy = -5(2+√3)(2+√3) = -5(2*2 + 2*2*√3) +√3*√3) = -5(4+4√3 +3)  

-5xy = - 5(7+4√3)

therefore,              3x^2-5xy-3y^2 = - 5(7+4√3)