Answer: t=2
Step-by-step explanation:
[tex]1=t+\sqrt{2t} -3\\1-1=t+\sqrt{2t}-3-1\\0= t+\sqrt{2t} -4\\Thus,\\t+\sqrt{2t} -4=0\\Let`s\ \sqrt{t} =x\geq 0\\\Rightarrow\ x^2+\sqrt{2} x-4=0\\x^2-\sqrt{2} x+2\sqrt{2}x-4=0\\ x(x-\sqrt{2})+2\sqrt{2} ( x-\sqrt{2})=0\\ (x-\sqrt{2})(x+2\sqrt{2})=0\\\\x-\sqrt{2} =0\\ x-\sqrt{2}+\sqrt{2}=0+\sqrt{2} \\ x=\sqrt{2}\\ \Rightarrow\ t=(\sqrt{2})^2\\ t=2\\\\x+2\sqrt{2} =0\\x+2\sqrt{2} -2\sqrt{2} =0-2\sqrt{2} \\x=-2\sqrt{2} \notin(x\geq 0)[/tex]
