Question

x²-2x-15=x²-25÷x²+10x+25=3x+9​

Answer 1

Respuesta:

$x=8,\:x=-3$

Explicación paso a paso:

$x^2-2x-15=3x+9\\\\x^2-2x-15-9=3x+9-9\\\\x^2-2x-24=3x\\\\x^2-2x-24-3x=3x-3x\\\\x^2-5x-24=0\\\\x_{1,\:2}=\frac{-\left(-5\right)\pm \sqrt{\left(-5\right)^2-4\cdot \:1\cdot \left(-24\right)}}{2\cdot \:1}\\\\\sqrt{\left(-5\right)^2-4\cdot \:1\cdot \left(-24\right)}\\\\=\sqrt{\left(-5\right)^2+4\cdot \:1\cdot \:24}\\\\\left(-5\right)^2=5^2\\\\=\sqrt{5^2+4\cdot \:1\cdot \:24}\\\\4\cdot \:1\cdot \:24=96\\\\=\sqrt{5^2+96}\\\\=\sqrt{25+96}\\\\25+96=121\\\\=\sqrt{121}\\\\=\sqrt{11^2}=11$

$x_{1,\:2}=\frac{-\left(-5\right)\pm \:11}{2\cdot \:1}\\\\x_1=\frac{-\left(-5\right)+11}{2\cdot \:1},\:x_2=\frac{-\left(-5\right)-11}{2\cdot \:1}\\\\\frac{-\left(-5\right)+11}{2\cdot \:1}=\frac{5+11}{2\cdot \:1}\\\\5+11=16=\frac{16}{2\cdot \:1}\\\\=\frac{16}{2}=8\\\\\frac{-\left(-5\right)-11}{2\cdot \:1}\\\\=\frac{5-11}{2\cdot \:1}\\\\5-11=-6\\\\2\cdot \:1=2\\\\=\frac{-6}{2}\\\\=\frac{-6}{2}=-3\\\\x=8,\:x=-3$