Question

A = {x: x² -3x +2 =0 }, B = {x : x³ -3x²+2x = 0 } तो A ∪ B ज्ञात कीजिए

Answer 1

हल - °•° A = {x : x² -3x +2 =0 }

•°• x² -3x + 2 = 0

x² -2x -x +2 =0

x(x-2) -1 (x-2) = 0

(x-2) (x-1)

अर्थात A = {1,2}

इसी प्रकार , B = {x : x³ -3x² +2x =0 }

x (x² -3x +2 ) = 0

x (x-2) (x-1) = 0

x = 0,1,2

अर्थात , B = {0,1,2}

तब, A ∪ B = {1,2} ∪ {0,1,2} = {0,1,2}

Answer 2

$\huge\boxed{\texttt{\fcolorbox{Red}{aqua}{Hey Mate!!!}}}$

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First we factories
$x {}^{2} - 3x + 2 = 0 \\ x {}^{2} - 2x - x + 2 = 0 \\ x(x - 2) - 1(x - 2) = 0 \\ (x - 2)(x - 1) = 0 \\ x = 2 \: and \: 1$
Hence
A = {1, 2}
Now
$x {}^{3} - 3x {}^{2} + 2x = 0 \\ x(x {}^{2} - 3x + 2x) = 0 \\ x(x {}^{2} - 2x - x + 2) = 0 \\ x(x(x - 2) - 1(x - 2)) = 0 \\ x(x - 2)(x - 1) = 0 \\ x = 0 \: \: . \: 1 \: \: and \: 2$
Hence
B= {0, 1, 2}

A. U B = {0, 1, 2 }


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