Question

X^4-3x²-10=0 ; x-5√x+6=0 решите два уравнения

Answer 1

$x^{4}-3x^{2}-10=0\\ x^{2}=t\\ t^{2}-3t-10=0\\ t_{1}+t_{2}=3\\ t_{1}t_{2}=-10\\ t_{1}=-2\\ t_{2}=5\\ x^{2}=-2 \to \varnothing\\ x^{2}=5 \to x=\pm\sqrt{5}$

ответ: $\pm \sqrt{5}$.

$x-5\sqrt{x}+6=0\\ (\sqrt{x})^{2}-5\sqrt{x}+6=0\\ \sqrt{x}=t\\ t^{2}-5t+6=0\\ t_{1}+t_{2}=5\\ t_{1}t_{2}=6\\ t_{1}=3\\ t_{2}=2\\ \sqrt{x}=2 \to x=4\\ \sqrt{x}=3 \to x=9$

ответ: 4, 9.

Answer 2

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