Question

Докажите тождество (х+1)(х+2)(х+3)(х+4)+1=(х^2+5х+5)^2

Answer 1

(x+1)(x+2)(x+3)(x+4)+1=(x²+5x+5)²

(x²+2x+x+2)(x+3)(x+4)+1=25+10x³+10x²+50x

x⁴+4x³+6x³+24x²+4x²+44x+6x+24=x⁴+25x²+25+10x³+10x²+5x

10x³+35x²+50x+25=35x²+25+10x³+50x