maths challenging questions

圖片參考：http://imgcld.yimg.com/8/n/HA00482599/o/701202140053813873437150.jpg

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but it is so complicated and i cannot understand well

hung is very professional.
Simon YAU, MSc Math

1)Put √(2+√(2+√(2+...)))=x________________√(2+x)=x___________________2+x=x²________________x²-x-2=0__________x²-x+1/4-9/4=0_ _ __(x-1/2)²-(3/2)²=0(x-1/2+3/2)(x-1/2-3/2)=0_ _ __ _ _ (x+1)(x-2)=0___________________x+1=0 or x-2=0_____________________x= -1 (neg., rej.) or 2_____________________x=2 2)Put_ 1/(1+1/(1+1/(1+...)))=x___________________1/(1+x)=x_________________________1=x+x²____________________x²+x-1=0______________x²+x+1/4-5/4=0_ _ ___ _(x+1/2)²-(√5/2)²=0_ [x+(1+√5)/2][x+(1-√5)/2]=0x+(1+√5)/2=0 or x+(1-√5)/2=0x= -(1+√5)/2 (neg., rej.) or (√5-1)/2x=(√5-1)/2