If X -2-3- XY -1- find the value of X -2- X - Y -2- Y

X/2 X + Y/2 Y = 2x xy+2y xy/(2 x)(2 y) = 2(x+y xy)/(2 x)(2 y)=A(Say) Now x = 2+√(3) xy = 1 ∴ y=1/2+√(3) = 2 √(3) ∴ x+y xy = 2+√̸(̸3̸)̸+2 √(3̸) 1=3 (1) (2 ...

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Byju's Answer

Standard VIII

Mathematics

Addition and Subtraction of Algebraic Expression

If X =2+√3, ...

Question

If $X = 2 + \sqrt{3}, X Y = 1$ , find the value of $\frac{X}{2 - X} + \frac{Y}{2 - Y}$

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Solution

$\frac{X}{2 - X} + \frac{Y}{2 - Y} = \frac{2 x - x y + 2 y - x y}{(2 - x) (2 - y)}$
$= \frac{2 (x + y - x y)}{(2 - x) (2 - y)} = A (S a y)$
$N o w x = 2 + \sqrt{3} x y = 1$
$∴ y = \frac{1}{2 + \sqrt{3}} = 2 - \sqrt{3}$
$∴ x + y - x y = 2 + / \sqrt{3} + 2 - \sqrt{/ 3} - 1 = 3$ - (1)
(2 - x) (2 - y) = 4 - 2x - xy + xy
= 4 - 2 (x + y) + xy
= 4 - 2 (4) + 1
= -3 ------(2)
$A = \frac{(1)}{(2)} = \frac{3}{- 3} = - 1$

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If X=2+√3, XY=1, find the value of X2−X+Y2−Y

X2−X+Y2−Y=2x−xy+2y−xy(2−x)(2−y) =2(x+y−xy)(2−x)(2−y)=A(Say) Now x=2+√3 xy=1 ∴ y=12+√3=2−√3 ∴ x+y−xy=2+/√3+2−√/3−1=3 - (1) (2 - x) (2 - y) = 4 - 2x - xy + xy = 4 - 2 (x + y) + xy = 4 - 2 (4) + 1 = -3 ------(2) A=(1)(2)=3−3=−1

If $X = 2 + \sqrt{3}, X Y = 1$ , find the value of $\frac{X}{2 - X} + \frac{Y}{2 - Y}$