Do you know that fish come out of eggs when they were born? After the baby fish comes out of the egg，it eats the food in the egg. When it is big enough，it leaves the egg. It swims in the water. You can see the eyes and the nose. Its ears are hidden (藏) in the head.

    Some fish eat other fish. The fish that eat plants have smaller mouths and teeth. The fish that eat other fish need larger mouths and stronger teeth.

Fish are usually dark on the top and light on the bottom.

阅读下面的材料，回答问题：

解方程x⁴﹣5x²+4=0，这是一个一元四次方程，根据该方程的特点，它的解法通常是：

设x²=y，那么x⁴=y²，于是原方程可变为y²﹣5y+4=0  ①，解得y₁=1，y₂=4．

当y=1时，x²=1，∴x=±1；当y=4时，x²=4，∴x=±2；

∴原方程有四个根：x₁=1，x₂=﹣1，x₃=2，x₄=﹣2．

（1）在由原方程得到方程①的过程中，利用什么法达到降次的目的，体现了数学的转化思想．

（2）解方程：（x²+3x）²+5（x²+3x）﹣6=0．

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设$F_1,F_2$分别为双曲线$\frac{x^2}{a^2}-\frac{y^2}{b^2}=1\left(a>0,b>0\right)$的左,右焦点.若在双曲线右支上存在一点P,满足$\left|P{F}_2\right|=\left|F_1{F}_2\right|$,且$F_2$到直线$P{F}_1$的距离等于双曲线的实轴长,则该双曲线的离心率为(   )