Question

Cho a + b = 5, ab = 6. Tính a² + b²

Answer 1

Ta có: \(a+b=5\)

\(\Rightarrow\left(a+b\right)^2=25\)

\(\Rightarrow a^2+2ab+b^2=25\)

\(\Rightarrow a^2+b^2+12=25\)

\(\Rightarrow a^2+b^2=13\).

Answer 2

Ta có: \(a+b=5\)

\(\Leftrightarrow\left(a+b\right)^2=5^2\)

\(\Leftrightarrow\left(a+b\right)^2=25\)

\(\Leftrightarrow a^2+2ab+b^2=25\)

Mà: \(ab=6\Rightarrow2ab=6\cdot2=12\)

Nên:\(a^2+2ab+b^2=25\)

\(\Leftrightarrow a^2+12+b^2=25\)

\(\Leftrightarrow a^2+b^2=25-12=13\)

Vậy \(a^2+b^2=13\)