If x(2-√3)=y(2-√3)=1,then find the value of 3x²-5xy-3y²
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Answer: -35-20×3^1/2
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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)
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