Ta có;
x+y=7
=>\(\left(x+y\right)^2=7^2\)
=>\(x^2+2xy+y^2=49\)
=>\(x^2+y^2=49-2xy=49-2.12=25\)
=>\(\left(x^2+y^2\right)^2=25^2\)
=>\(x^4+2\left(xy\right)^2+y^4=25^2\)
=>\(x^4+y^4=625-2\left(xy\right)^2=625-2.12^2=625-288=337\)
Vậy...
Ta có:
\(x+y=7\Rightarrow\left(x+y\right)^2=49\)
\(\Leftrightarrow x^2+y^2=49-2xy\)
\(\Leftrightarrow x^2+y^2=49-24=25\)
\(\Leftrightarrow\left(x^2+y^2\right)^2=25^2=625\)
\(\Leftrightarrow x^4+2x^2y^2+y^4=625\)
\(\Leftrightarrow x^4+y^4+2.\left(xy\right)^2=625\)
\(\Leftrightarrow x^4+y^4+288=625\)
\(\Leftrightarrow x^4+y^4=625-288=337\)
Chúc bạn học tốt^^!
Theo đề bài ra ta có :
\(x+y=7\)
\(\Rightarrow\left(x+y\right)^2=49\)
\(\Rightarrow x^2+2xy+y^2=49\)
\(\Rightarrow x^2+y^2=49-2xy\)
\(\Rightarrow x^2+y^2=25\)
\(\Rightarrow\left(x^2+y^2\right)^2=25^2\)
\(\Rightarrow x^4+2\left(xy\right)^2+y^4=25^2\)
\(\Rightarrow x^4+y^4=625-2\left(xy\right)^2=625-2.12^2=377\)
Vậy \(x^4+y^4=377\)
\(x+y=7\)
\(\Rightarrow\left(x+y\right)^2=49\)
\(\Rightarrow x^2+2xy+y^2=49\)
Vì \(xy=12\) nên \(2xy=24\)
\(\Rightarrow x^2+2xy+y^2-2xy=49-24\)
\(\Rightarrow x^2+y^2=25\)
\(\Rightarrow\left(x^2+y^2\right)^2=625\)
\(\Rightarrow x^4+2\left(xy\right)^2+y^4=625\)
Vì \(xy=12\) nên \(2\left(xy\right)^2=288\)
\(\Rightarrow x^4+2\left(xy\right)^2+y^4-2\left(xy\right)^2=625-288\)
\(\Rightarrow x^4+y^4=337\)