Question

x19-x7=17625 what is possible valueof x

Answer 1

The possible value of $x$ is $4.0419$ and $2.2586$

Step-by-step explanation:

Given equation: $x^{19}-x^{7}=17625$

∴ $x^{19}-x^{7}=17625$

⇒$x^{7}(x^{12}-1)=17625$

∴ $x^{7}=17625$ and $x^{12}-1=17625$

Now, We solve,

$x^{7}=17625$

⇒$x=\sqrt[7]{17625}$

⇒$x=4.0419$

And,

$x^{12}-1=17625$

⇒$x^{12}=17625+1$

⇒$x^{12}=17626$

⇒$x=\sqrt[12]{17626}$

⇒$x=2.2586$

Hence, The possible value of $x$ is $4.0419$ and $2.2586$