Question

Решить уравнение
$(sqrt{4+ sqrt{15} } )^{x} + (sqrt{4- sqrt{15} } )^{x} = 8$

Answer 1

$(sqrt{4+sqrt{15}})^x+(sqrt{4-sqrt{15}})^x=8\ 4+sqrt{15}=a\ 4-sqrt{15}=frac{1}{a}\ tak kak frac{(4+sqrt{15})(4-sqrt{15})}{4-sqrt{15}}=frac{1}{4-sqrt{15}}\ sqrt{a}^x+sqrt{frac{1}{a}}^x=8\ a^x+frac{1}{a^x}+2=64\ vozvel v kvadrat\ a^{2x}-62a^x+1=0\ a^x=t\ t^2-62t+1=0\ t=8sqrt{15}+31\ (4+sqrt{15})^x=8sqrt{15}+31\ x=2$