X- -5 - 2-5 - 2 and y- -5 - 2-5 - 2-Find the value of xy-

Given, y = √( 5 ) +2 /√( 5 ) 2 , x=√( 5 ) 2 /√( 5 ) +2 . x× y = √( 5 ) +2 /√( 5 ) 2 ×√( 5 ) 2 /√( 5 ) +2 ∴ x× y= 1 . ...

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Expansion of (x^2 - y^2)

x= √5 - 2/√5 ...

Question

$x = \frac{\sqrt{5} - 2}{\sqrt{5} + 2}$ and $y = \frac{\sqrt{5} + 2}{\sqrt{5} - 2}$ .
Find the value of $x y$ .

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Solution

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x = \frac{\sqrt{5} - 2}{\sqrt{5} + 2}

y = \frac{\sqrt{5} + 2}{\sqrt{5} - 2}

x + y

x = \frac{\sqrt{5} - 2}{\sqrt{5} + 2}

y = \frac{\sqrt{5} + 2}{\sqrt{5} - 2}

x^{2} + y^{2} + x y

x^{2} + y^{2} = 14

x y = 3

2 (x + y)^{2} - 5 (x - y)^{2}

Find the equation of the bisectors of the angle between the lines represented by $3 x^{2} - 5 x y + 4 y^{2} = 0$

x + y = 3, x y = 5

x^{2} + y^{2}

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