Question

Si P(x+2)=2x²-3x+5 calcula P(0)​

Answer 1

Respuesta:

$x=\frac{3+P+\sqrt{P^2+22P-31}}{4},\:x=\frac{3+P-\sqrt{P^2+22P-31}}{4}$

Explicación paso a paso:

$P\left(x+2\right)=2x^2-3x+5\\\\xP+2P=2x^2-3x+5\\\\2x^2-3x+5=xP+2P\\\\2x^2-3x+5=xP+2P\\\\2x^2-3x+5-2P=xP\\\\2x^2-3x+5-2P-xP=xP-xP\\\\2x^2-\left(3+P\right)x+5-2P=0$

Con la formula

$x_{1,\:2}=\frac{-\left(-3-P\right)\pm \sqrt{\left(-3-P\right)^2-4\cdot \:2\left(5-2P\right)}}{2\cdot \:2}\\\\x_{1,\:2}=\frac{-\left(-3-P\right)\pm \sqrt{P^2+22P-31}}{2\cdot \:2}\\\\x_1=\frac{-\left(-3-P\right)+\sqrt{P^2+22P-31}}{2\cdot \:2},\:x_2=\frac{-\left(-3-P\right)-\sqrt{P^2+22P-31}}{2\cdot \:2}\\\\x=\frac{3+P+\sqrt{P^2+22P-31}}{4},\:x=\frac{3+P-\sqrt{P^2+22P-31}}{4}$

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