Question

Scrieți următoarele numere ca sume pătrate: 34; 50; 100; 3x^2+1; x^2+6x+34; x^2+2x+y^2+4y+6; x^2+10x+y^2-4y+30; 5x^2-2x+14; 4x^2 +5y^2-8xy-6y+9

Answer 1

34=25+9=5²+3²

50=49+1=7²+1 ²

100=64+36=8²+6²

3x²+1=x²+x²+x²+1²

x²+6x+34=(x²+6x+9)+25=(x+3)²+5²

x²+2x+y²+4y+6=(x²+2x+1)+(y²+4y+4)+1=(x+1)²+(y+2)²+1²

x²+10x+y²-4y+30=(x²+10x+25)+(y²-4y+4)+1=(x+5)²+(y-2)²+1²

5x²-2x+14=4x²+(x²-2x+1)+4+9=(2x)²+(x-1)²+2²+3²

4x² +5y²-8xy-6y+9=(4x²-8xy+4y^2)+(y²-6y+9)=(2x-2y)²+(y-3)²