Find the set of solutions for equation 2sinX m 1 m not 0

Solution: i) When m 0, m+1 m 2, and if and only if m=1, take the equal sign to get 2sinx 2 sinx 1 sinx=1x=2k + 2

ii) When m 0, m+1 m -2, and if and only if m = -1, take the equal sign to get 2sinx -2 sinx -1 sinx=-1x=2k - 2

To sum up: m=1, x=2k + 2

m=-1, x=2k - 2

m≠ 1 and m≠0, there is no solution.

When m>0 there is m+1 m>=2 if and only if m=1, take the equal sign.

When m>0 there is m+1 m>=2 if and only if m=1, take the equal sign.

However, 2sinx belongs to [-2,2].

Its solution must have sinx=1 sinx=-1x = pai 2 + 2k*pai or x = - pai 2 + 2k*pai k is an arbitrary integer.

If m is positive, then m+1 m>=2;If m is negative, then m+1 m<=-2;

And 2sinx is between -2 and 2, so m+1 m can only be equal to 2 or -2, so m is 1 or -1, and the solution set is .

2sinx=m+1 m is greater than or equal to 2 you know? According to a + b greater than or equal to 2 and the root number ab to get m+1 m greater than or equal to 2i.e. 2sinx is greater than or equal to 2

sinx is greater than or equal to 1, that is, sinx=1So the solution set for x is 2+2k(k is a natural number).

From the inscription x1=-2, x2=-1 is Fang Jianqin's shouting of the first rock Cheng two solutions.

substitution. 4-2m+n=0

1-m+n=0

Solve this equation to obtain the wild group.

m=3,n=2

The solution set of the equation x 2 +mx+n=0(m,n r) is, -2,-1 are the two central real roots of the equation x 2 +mx+n=0(m,n r).

-2-1=-m, -2 (-1)=n, m=3, and n=2

So the answers are: 3; 2．

From the meaning of the title, it is known that is the equation x2

mx+n=0, -2+1=-m, -2 1=n, respectful.

Burning bucket m=1, n=-2, leather grinding m+n=-1 so the answer is -1

m Hall 2, Ant Bridge 2-m 0, then (2-m) x m-2, muffled and fierce.

x＞（m-2）/（2-m）

i.e. x -1

From (2m-n) x-m-5n>0 obtains: x>(m+5n) (2m-n), i.e., 10 7> carrying round J x>(m+5n) (2m-n), obtains: 10 7>(m+5n) (2m-n).

Cavity solution: 13m>45ni.e. 13 45>n m by mx

(m-2)x1 (multiply or divide two equal negative numbers on both sides of the inequality at the same time, and the direction of the unequal sign changes).

Both sides of the inequality are divided by m-2 at the same time

But m<2 gets m-2<0

Divide both sides of the inequality by a number less than 0 at the same time, and the unequal sign changes direction.

So x 1

Since m<2, m-2<0, so both sides are divided by m-2 at the same time, and the unequal sign changes, so x>1

Solution: Because m<2, then m-2<0, so (m-2)x(m-2) (m-2).

So the solution is:

Bringing -1 into gives m+2-3=0 so m=1 brings in the original inequality x 2x 3 0

The solution gives -1 x 3 so n=3

So m+2n=1+2*3=7