請各位快來幫幫我吧!有些數學題不會。1. 555^2+111^2=666^2-222*? 2. 老師今年(3x+7)歲，學生3年前x歲，經過x年後，老師與學生相差幾歲? 3. 3^2/(2^2-1)*4^2(3^-1)*5^2/(4^2-1)*...*19^2/18^-1)=?

1. 555^2+111^2=666^2-222*?
Sol
p=111
555^2+111^2+222^2-666^2
=(5p)^2+p^2+(2p)^2-(6p)^2
=-6p^2<0
555^2+111^2<666^2-222^2
2
Sol
老師今年(3x+7)歲
學生今年(x+3)歲
今年老師與學生相差(2x+4)歲
x年後老師與學生相差(2x+4)歲
3
Sol
3^2/(2^2－1)*4^2/(3^2－1)*5^2/(4^2－1)*...*19^2/(18^2－1)
=3^2/(1*3)*4^2/(2*4)*5^2/(3*5)*...*19^2/(17*19)
=(3/1)*(4/2)*(5/3)*...*(19/17)
=(3/1)*(4/2)*(5/3)*(6/4)*(7/5)*…*(15/13)*(16/14)*(17/15)*(18/16)*(19/17)
=(1/1)*(1/2)*(1/1)*(1/1)*(1/1)*…*(1/1)*(1/1)*(1/1)*(18/1)*(19/1)
=171