Question

Giải phương trình: \(\dfrac{1}{y^2-3y+2}+\dfrac{1}{y^2-5y+6}+\dfrac{1}{y^2-7y+12}+\dfrac{1}{y^2-9y+20}=\dfrac{1}{15}\)

Answer 1

sory doan cuoi minh lam sai minh lam lai nhe

pt<=>1/(y-1)(y-2) + 1/(y-2)(y-3) + 1/(y-3)(y-4) + 1(y-4)(y-5)=1/15

=>1/(y-1) -1/(y-2)+1/(y-2)-1/(y-3)+1/(y-3)-1/(y-4)+1/(y-4)-1/(y-5)=1/15

=>1/(y-1) - 1/(y-5)=1/15

=>4/(y-1)(y-5)=1/15

=> (y-1)(y-5)=60

=> y²-6y+5-60=0

=>y²-6y-55=0

=> (y-11)(y+5)=0

=>y=11 hoac y=-5

Answer 2

pt<=> 1/(y-1)(y-2) + 1/(y-2)(y-3) + 1/(y-3)(y-4) + 1/(y-4)(y-5)=1/15

=>1/(y-1)-1/(y-2)+1/(y-2)-1/(y-3)+1/(y-3)-1/(y-4)+1/(y-4)-1/(y-5)=1/15

=>1/(y-1)-1/(y-5)=1/15

=>(y-1)(y-5)=-4.15=-60

=>y²-6y+65=0 k tim dc nghiem