Question

tìm x,y 

  a, x.(x+1)=30     b, x.y=15 và x>y

Answer 1

a: x(x+1)=30

=>\(x^2+x=30\)

=>\(x^2+x-30=0\)

=>\(x^2+6x-5x-30=0\)

=>\(x\left(x+6\right)-5\left(x+6\right)=0\)

=>(x+6)(x-5)=0

=>\(\left[{}\begin{matrix}x+6=0\\x-5=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-6\\x=5\end{matrix}\right.\)

b: xy=15

=>\(x\cdot y=1\cdot15=15\cdot1=\left(-1\right)\cdot\left(-15\right)=\left(-15\right)\cdot\left(-1\right)=3\cdot5=5\cdot3=\left(-3\right)\cdot\left(-5\right)=\left(-5\right)\cdot\left(-3\right)\)

mà x>y

nên \(\left(x,y\right)\in\left\{\left(15;1\right);\left(-1;-15\right);\left(5;3\right);\left(-3;-5\right)\right\}\)