Question

cho x+y=7; x^2+y^2=25 tính x^4+y^4; x^5+y^5

giúp mik zới

 

 

Answer 1

Ta có \(\left(x+y\right)^2=x^2+2xy+y^2=49\Leftrightarrow xy=\dfrac{49-25}{2}=12\)

\(x^4+y^4=\left(x^2+y^2\right)^2-2x^2y^2=25^2-2\cdot12^2=337\)

Ta có \(x^3+y^3=\left(x+y\right)^3-3xy\left(x+y\right)=7^3-3\cdot12\cdot7=91\)

\(\left(x^2+y^2\right)\left(x^3+y^3\right)=91\cdot25=2275\\ \Leftrightarrow x^5+y^5+2x^2y^2\left(x+y\right)=2275\\ \Leftrightarrow x^5+y^5=2275-2\cdot144\cdot7=259\)