Question

1=t +√2t-3. please show your working ​

Answer 1

Answer: t=2

Explanation:

`1=t+√(2t) -3\\1-1=t+√(2t)-3-1\\0= t+√(2t) -4\\Thus,\\t+√(2t) -4=0\\Let`s\ √(t) =x\geq 0\\\Rightarrow\ x^2+√(2) x-4=0\\x^2-√(2) x+2√(2)x-4=0\\ x(x-√(2))+2√(2) ( x-√(2))=0\\ (x-√(2))(x+2√(2))=0\\\\x-√(2) =0\\ x-√(2)+√(2)=0+√(2) \\ x=√(2)\\ \Rightarrow\ t=(√(2))^2\\ t=2\\\\x+2√(2) =0\\x+2√(2) -2√(2) =0-2√(2) \\x=-2√(2) \\otin(x\geq 0)`