Question

15 баллов. Срочнооо​

Answer 1

ОДЗ : x + 1 ≥ 0     ⇒    x ≥ - 1

$14*4^{\sqrt{x+1}}+3*14^{\sqrt{x+1}}-2*49^{\sqrt{x+1}}=0\\\\\frac{14*4^{\sqrt{x+1}}}{4^{\sqrt{x+1}}}+\frac{3*14^{\sqrt{x+1}}}{4^{\sqrt{x+1}}}-\frac{2*49^{\sqrt{x+1}}}{4^{\sqrt{x+1}}}=0\\\\14+3*(\frac{7}{2})^{\sqrt{x+1}}-2*[( \frac{7}{2})^{\sqrt{x+1}}]^{2}=0\\\\(\frac{7}{2})^{\sqrt{x+1}}=m,m>0\\\\14+3m-2m^{2}=0\\\\2m^{2}-3m-14=0\\\\D=(-3)^{2}-4*2*(-14)=9+112=121=11^{2}\\\\m_{1}=\frac{3+11}{4}=\frac{7}{2}\\\\m_{2}=\frac{3-11}{4}=-2<0-neyd\\\\(\frac{7}{2})^{\sqrt{x+1}}=\frac{7}{2}$

$\sqrt{x+1}=1\\\\x+1=1\\\\x=0\\\\Otvet:\boxed{0}$