Question

a : b = 3 : 4.    a² + b² = 36  tìm hai số

Cách giải rõ ràng

Answer 1

ta kó:  a:b=3:4 => \(\frac{a}{3}=\frac{b}{4}\)=>\(\frac{a^2}{9}=\frac{b^2}{16}\)=\(\frac{a^2+b^2}{9+16}=\frac{36}{25}\)\(=\left(\frac{6}{5}\right)^2\)

=>a²/9 =(6/5)² =>(a/3)²=(6/5)² =>a/3=6/5 hoặc a/3=-6/5

    a/3=6/5 =>5a=18 =>a=18/5

    a/3=-6/5 =>5a=-18=>a=-18/5

=>b²/16=(6/5)² =>(b/4)²=(6/5)²=>b/4=6/5 hoặc b/4=-6/5

     b/4=6/5 =>5b=24=>b=24/5

     b/4=-6/5 =>5a=-24=>a=-24/5

vậy a=18/5 ; b=24/5

hoặc a=-18/5; b=-24/5