Question

If and , find the value of .
Answer:

Answer 1

\(a^3+b^3=637\Leftrightarrow\left(a+b\right)\left(a^2-ab+b^2\right)=637\Rightarrow a^2-ab+b^2=\frac{637}{13}=49\)\(\left(a+b\right)=13\Rightarrow\left(a+b\right)^2=13^2=169\Leftrightarrow a^2+2ab+b^2=169\)

Ta có: \(a^2-ab+b^2=49\left(1\right)\)

\(a^2+2ab+b^2=169\left(2\right)\)

Lấy (2) trừ 1 ta được 3ab=120=>ab=40

ab=40=>-ab=-40=>a²+b²=49+40=89

\(\left(a-b\right)^2=a^2-2ab+b^2=a^2+b^2-2ab=89-2.40=89-80=9\)Nhập kết quả: 9

Answer 2

9