Question

Tìm các số hữu tỉ a, b, c thỏa mãn:

a, a\(\times\)b=\(\frac{3}{5}\), b\(\times\)c=\(\frac{4}{5}\), c\(\times\)a=\(\frac{3}{4}\)

b, a\(\times\)(a+b+c)=-12, b\(\times\)(a+b+c)=18, c\(\times\)(a+b+c)=30

Answer 1

a, Ta có : \(\left(abc\right)^2=\frac{3}{5}.\frac{4}{5}.\frac{3}{4}=\frac{9}{25}\)

=> \(abc=\frac{3}{5}\)

Mà ab = 3/5

=> c = 1.

=> \(\left\{{}\begin{matrix}b=\frac{4}{5}\\a=\frac{3}{4}\end{matrix}\right.\)

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b, Ta có : \(a\left(a+b+c\right)+b\left(a+b+c\right)+c\left(a+b+c\right)=36\)

=> \(\left(a+b+c\right)^2=36\)

=> a + b + c = 6.

=> \(\left\{{}\begin{matrix}a=-\frac{12}{6}=-2\\b=\frac{18}{6}=3\\c=\frac{30}{6}=5\end{matrix}\right.\)

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