Đáp án:
`a^2+b^2 = 61`
`⇔ (a^2+2ab+b^2)-2ab = 61`
`⇔ (a+b)^2 = 61+2ab`
`⇔ (a+b)^2 = 61+2.30`
`⇔ (a+b)^2 = 61+60`
`⇔ (a+b)^2 = 121`
`⇔ a+b = ±11`
⇔ \(\left[ \begin{array}{l}a=11-b\\a=-11-b\end{array} \right.\)
`a.b = 30`
`⇒ TH1 : (11-b).b = 30`
`⇔ 11b-b^2-30 = 0`
`⇔ (11b-55)-(b^2-25)=0`
`⇔ 11(b-5)-(b-5)(b+5) = 0`
`⇔ (b-5)(11-b-5) = 0`
`⇔ (b-5)(6-b) = 0`
⇔ \(\left[ \begin{array}{l}b-5=0\\6-b=0\end{array} \right.\)
⇔ \(\left[ \begin{array}{l}b=5\\b=6\end{array} \right.\)
⇒ \(\left[ \begin{array}{l}a=6\\a=5\end{array} \right.\)
`TH2 : (-11-b).b = 30`
`⇔ -11b-b^2-30 = 0`
`⇔(-11b-55)-(b^2-25) = 0`
`⇔ -11(b+5)-(b-5)(b+5) = 0`
`⇔ (b+5)(-11-b+5) = 0`
`⇔ (b+5)(-6-b) = 0`
⇔ \(\left[ \begin{array}{l}b+5=0\\-6-b=0\end{array} \right.\)
⇔ \(\left[ \begin{array}{l}b=-5\\b=-6\end{array} \right.\)
⇒ \(\left[ \begin{array}{l}a=-6\\a=-5\end{array} \right.\)
+Vậy `(a;b) = (5;6) ; (6;5) ; (-5;-6) ; (-6;-5)`
