Question

if A={x:x belongs to z, x^4-16=0},then​

Answer 1

$Given \: A = \{x: x \in Z , x^{4} - 16 = 0 \}$

$x^{4} - 16 = 0$

$\implies (x^{2})^{2} - 4^{2} = 0$

$\implies (x^{2} + 4)( x^{2} - 4 ) = 0$

$\implies (x^{2} + 4 )(x^{2} - 2^{2} ) = 0$

$\implies (x^{2} + 4 )(x+2)(x-2)= 0$

$\implies x^{2} + 4 = 0\: Or \: x+2= 0 \:Or \:x-2=0$

$\implies x^{2} = - 4 \: Or \: x = -2 \:Or \:x=2$

Therefore.,

$\red { A } \green { = \{ -2,2 \}}$

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