Question

escreva na forma ax²+bx+c=0

A) 2x²-1/3=x²

B) x²/4+1/10=x²/5+x/2

C)2x/x-3=x+1/x+3

por favor me ajudem vale 20 pontos

Answer 1

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$\tt a)~\sf\dfrac{2x^2-1}{3}=x^2\\\sf 3x^2=2x^2-1\\\sf 3x^2-2x^2+1=0\\\huge\boxed{\boxed{\boxed{\boxed{\boxed{\sf x^2+1=0}}}}}$

$\tt b)~\sf\dfrac{x^2}{4}+\dfrac{1}{10}=\dfrac{x^2}{5}+\dfrac{x}{2}\cdot(20)\\\sf \diagup\!\!\!\!\!20^5\cdot\dfrac{x^2}{\diagup\!\!\!4}+\diagup\!\!\!\!\!20^2\cdot\dfrac{1}{\diagup\!\!\!\!\!10}=\diagup\!\!\!\!\!20^4\cdot\dfrac{x^2}{\diagup\!\!\!\!5}+\diagup\!\!\!\!\!20^{10}\cdot\dfrac{x}{\diagup\!\!\!2}\\\sf5x^2+2=4x^2+10x\\\sf5x^2-4x^2-10x+2=0\\\huge\boxed{\boxed{\boxed{\boxed{\sf x^2-10x+2=0\checkmark}}}}$

$\tt c)~\sf\dfrac{2x}{x-3}=\dfrac{x+1}{x+3}\implies 2x\cdot(x+3)=(x-3)\cdot(x+1)\\\sf 2x^2+6x=x^2+x-3x-3\\\sf 2x^2-x^2+6x-x+3x+3=0\\\huge\boxed{\boxed{\boxed{\boxed{\sf x^2+8x+3=0\checkmark}}}}$