[(x+ 1)(x+4)][(x+2)(x+3)]= 24

(x？ +5x+4)(x？ +5x+6)=24

(x？ +5 times)? + 10(x？ +5x)+24=24

(x？ +5 times)? + 10(x？ +5x)=0

(x？ +5x+ 10)(x？ +5x)=0

And what about x? +5x+ 10=(x+5/2)？ +15/4 >0 holds.

∴x？ +5x=0 ∴ x 1=0，x2=-5。

( 12)x？ -2xy-3y？ =0

(x-3y)(x+y)=0

∴x=3y or x=-y

When x=3y, (2x+3y)/(3y)=3.

When x=-y, (2x+3y)/(3y)= 1/3.

(13)∵BC, is AC a univariate quadratic equation about X? Two roots of -2(m- 1)x+m(m-2)=0.

According to the relationship between root and coefficient, BC+AC = 2 (m- 1) BC AC = m (m-2).

AB is the hypotenuse of Rt△ABC, and BC and AC are right angles.

∴AB？ =BC？ +AC？ =(BC+AC)？ -2BC AC=4(m- 1)？ -2m(m-2)=2m？ +4m+4= 10

∴m？ +2m-3=0 gives m= 1 or m=-3.

And △=[2(m- 1)]? -4m(m-2)=4

So the value of m that satisfies the meaning of the question is -3 or 1.