Toán Lớp 9: Tìm a và b biết $a^{2}+b^{2}=61$ và $ab=30$

Question

Toán Lớp 9:  Tìm a và b biết  $a^{2}+b^{2}=61$ và $ab=30$

tuenhioanh · Answer

Giải đáp:        a^2+b^2 = 61   &hArr; (a^2+2ab+b^2)-2ab = 61   &hArr; (a+b)^2 = 61+2ab   &hArr; (a+b)^2 = 61+2.30   &hArr; (a+b)^2 = 61+60   &hArr; (a+b)^2 = 121   &hArr; a+b = &plusmn;11   &hArr;  ( left[  begin{array}{l}a=11-b  a=-11-b end{array}  right. )          a.b = 30   &rArr; TH1 : (11-b).b = 30   &hArr; 11b-b^2-30 = 0   &hArr; (11b-55)-(b^2-25)=0   &hArr; 11(b-5)-(b-5)(b+5) = 0   &hArr; (b-5)(11-b-5) = 0   &hArr; (b-5)(6-b) = 0   &hArr;  ( left[  begin{array}{l}b-5=0  6-b=0 end{array}  right. )    &hArr;  ( left[  begin{array}{l}b=5  b=6 end{array}  right. )    &rArr;  ( left[  begin{array}{l}a=6  a=5 end{array}  right. )    TH2 : (-11-b).b = 30   &hArr; -11b-b^2-30 = 0   &hArr;(-11b-55)-(b^2-25) = 0   &hArr; -11(b+5)-(b-5)(b+5) = 0   &hArr; (b+5)(-11-b+5) = 0   &hArr; (b+5)(-6-b) = 0   &hArr;  ( left[  begin{array}{l}b+5=0  -6-b=0 end{array}  right. )    &hArr;  ( left[  begin{array}{l}b=-5  b=-6 end{array}  right. )    &rArr;  ( left[  begin{array}{l}a=-6  a=-5 end{array}  right. )    +Vậy (a;b) = (5;6) ; (6;5) ; (-5;-6) ; (-6;-5)