Rozwiąż nierówność:
a)
x\sqrt2-3=x-1
x\sqrt2-x=3-1
x(\sqrt2-1)=2/:(\sqrt2-1)
x=\frac{2}{\sqrt2-1}*\frac{\sqrt2+1}{\sqrt2+1}
x=\frac{2\sqrt2+2}{\sqrt2^2-1^2}
x=2\sqrt2+2
x=2(\sqrt2+1)
b)
x+(1+x)\sqrt5=1
x+\sqrt5+\sqrt5x=1
x+\sqrt5x=1-\sqrt5
x(1+\sqrt5)=1-\sqrt5/:(1+\sqrt5)
x=\frac{1-\sqrt5}{1+\sqrt5}*\frac{1-\sqrt5}{1-\sqrt5}
x=\frac{1-\sqrt5-\sqrt5+5}{1^2-\sqrt5^2}
x=\frac{6-2\sqrt5}{-4}
x=\frac{-2(-3+\sqrt5)}{-4}=\frac{\sqrt5-3}{2}