Question

hola , podrían ayudarme con esto?.​

Answer 1

Respuesta:

regalame la coronita =<

Explicación paso a paso:

$10^2=x^2+\left(x+2\right)^2\\\\100=2x^2+4x+4\\\\2x^2+4x+4=100\\\\2x^2+4x+4-100=100-100\\\\2x^2+4x-96=0\\\\x_{1,\:2}=\frac{-4\pm \sqrt{4^2-4\cdot \:2\left(-96\right)}}{2\cdot \:2}\\\\x_{1,\:2}=\frac{-4\pm \:28}{2\cdot \:2}\\\\x_1=\frac{-4+28}{2\cdot \:2},\:x_2=\frac{-4-28}{2\cdot \:2}\\\\x=6,\:x=-8$

No olvidemos la formula del cuadrado de un binomio:

$\left(x+2\right)^2=x^2+4x+4\\\\x^2+4x+4=x^2+4x+4\\\\x^2+4x+4-4=x^2+4x+4-4\\\\x^2+4x=x^2+4x\\\\x^2+4x-\left(x^2+4x\right)=x^2+4x-\left(x^2+4x\right)\\\\0=0$

Sustituyendo

$100=x^2+x^2+4x+4\\\\100=2x^2+4x+4\\\\2x^2+4x+4=100\\\\2x^2+4x+4-100=100-100\\\\2x^2+4x-96=0\\\\x_{1,\:2}=\frac{-4\pm \sqrt{4^2-4\cdot \:2\left(-96\right)}}{2\cdot \:2}\\\\x_{1,\:2}=\frac{-4\pm \:28}{2\cdot \:2}\\\\x_1=\frac{-4+28}{2\cdot \:2},\:x_2=\frac{-4-28}{2\cdot \:2}\\\\x=6,\:x=-8$

Simplificamos la ecuacion:

$2x^2+4x-96=0\\\\x_{1,\:2}=\frac{-4\pm \sqrt{4^2-4\cdot \:2\left(-96\right)}}{2\cdot \:2}\\\\x_{1,\:2}=\frac{-4\pm \:28}{2\cdot \:2}\\\\x_1=\frac{-4+28}{2\cdot \:2},\:x_2=\frac{-4-28}{2\cdot \:2}\\\\x=6,\:x=-8$