Question

Ajuda em equações do 2 grau:
A) 8x² = 60-7x²
B) 3( x² -1) = 24
C) 3x²+30=0
D) 16= 9x²
E) 5 ( x² -1)= 4 ( x²+1)

Answer 1

$A) 8 x^{2} = 60-7 x^{2} \to 8 x^{2} +7 x^{2} =60\to 15 x^{2} =60\to x^{2} = \frac{60}{15} \to \\\\ x^{2} =4\to x=\pm \sqrt{4} \to x=\pm 2\\\\\\ S=(-2;2)$





$B) 3( x^{2} -1) = 24\to 3 x^{2} -3=24\to 3 x^{2} =24+3\to 3 x^{2} =27\\\\ x^{2} = \frac{27}{3} \to x^{2} =9\to x=\pm \sqrt{9}\to x=\pm 3 \\\\\\ S=(-3;3)$





$C) 3 x^{2} +30=0\to 3 x^{2} =-30\to x^{2} = \frac{-30}{3} \to x^{2} =-10\to x=\pm \sqrt{-10}$

Não existe solução real para essa equação, portanto, S={   }.





$D) 16= 9 x^{2} \to \frac{16}{9} = x^{2} \to x^{2} =\pm \sqrt{ \frac{16}{9}} \to x\pm \frac{4}{3}\\\\ \\ S=(-\frac{4}{3};\frac{4}{3})$





$E) 5 ( x^{2} -1)= 4 ( x^{2} +1)\to 5 x^{2} -5=4 x^{2} +4\to 5 x^{2} -4 x^{2} =4+5\to \\\\ x^{2} =9\to x=\pm \sqrt{9} \to x=\pm 3\\\\\\ S=(-3;3)$