Question

solve x2+ (√3+1)x +√5 from ch quatic equations class 10​

Answer 1

Step-by-step explanation:

$\tt\implies \: x^{2}+\left(\sqrt{3}+1\right)x+\sqrt{5}=0$

$\tt\implies \: x=\dfrac{-\left(\sqrt{3}+1\right)±\sqrt{\left(\sqrt{3}+1\right)^{2}-4\sqrt{5}}}{2}$

$\tt\implies x=\dfrac{-\left(\sqrt{3}+1\right)±\sqrt{2\sqrt{3}+4-4\sqrt{5}}}{2}$

$\tt\implies x=\dfrac{-\left(\sqrt{3}+1\right)±i\sqrt{4\sqrt{5}-2\sqrt{3}-4}}{2}$

$\red{ \tt\implies \:x=\frac{-\sqrt{3}-1+i\sqrt{4\sqrt{5}-2\sqrt{3}-4}}{2}} \\ \orange{ \tt \implies x=\frac{-i\sqrt{4\sqrt{5}-2\sqrt{3}-4}-\sqrt{3}-1}{2} }$