Question

Alguém pode me ajudar com algumas questões de equação do 2° grau? Quem puder me ajudar, agradeço desde já
a)9x²-x+2=0
b)x²+14x-32=0
c)9x²+16x-64=0
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Answer 1

Olá, boa tarde!

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$9x^2-x+2=0\\\\Coeficientes:\;a=9\;b=-1\;e\;c=2\\\\\Delta=b^2-4ac\\\Delta=(-1)^2-4\cdot9\cdot2\\\Delta=1-72\\\Delta=-71$

A equação não possui solução no conjunto dos números reais.

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$x^2+14x-32=0\\\\Coeficientes:\;a=1\;b=14\;e\;c=-32\\\\\Delta=b^2-4ac\\\Delta=(14)^2-4\cdot1\cdot(-32)\\\Delta=194+128\\\Delta=324\\\\x=\dfrac{-b\pm\sqrt{\Delta}}{2a}\\\\x=\dfrac{-14\pm\sqrt{324}}{2\cdot1}\\\\x=\dfrac{-14\pm18}{2}\\\\x_1=\dfrac{-14+18}{2}=\dfrac{4}{2}=\boxed{2}\\\\x_2=\dfrac{-14-18}{2}=\dfrac{-32}{2}=}\boxed{-16}$

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$9x^2+16x-64=0\\\\Coeficientes:\;a=9\;b=16\;e\;c=-64\\\\\Delta=b^2-4ac\\\Delta=(16)^2-4\cdot9\cdot(-64)\\\Delta=256+2304\\\Delta=2560\\\\x=\dfrac{-b\pm\sqrt{\Delta}}{2a}\\\\x=\dfrac{-16\pm\sqrt{2560}}{2\cdot9}\\\\x=\dfrac{-16\pm\sqrt{2^2\cdot2^2\cdot2^2\cdot2^2\cdot10}}{18}\\\\x=\dfrac{-16\pm16\sqrt{10}}{18}\\\\x_1=\dfrac{-16+16\sqrt{10}}{18}=\boxed{\dfrac{-8+8\sqrt{10}}{9}}\\\\x_2=\dfrac{-16-16\sqrt{10}}{18}=\boxed{\dfrac{-8-8\sqrt{10}}{9}}$

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Espero ter ajudado.

Bons estudos! :)