Algebra on discriminant theorems

First, from the discriminant formula of the quadratic equation δ b 2-4ac, we get:

25+4（m^2-1）

21+4m^2 >0

From the root finding formula, we get a=x1 5+ (21 4m 2) 2 , obviously a>0

b=x2＝〔5－√（21＋4m^2）〕/2

If, 5 (21 4m2) then b 0, then.

a + b = 5 6 conditions are met.

At this time, 5 (21 4m 2), so the solution gives -1 m 1

If, 5 (21 4m2) then b<0, at this time, m<-1 or m>1 then.

a + b = (21 4m 2) 6, solution.

15/4)≤ m ≤√15/4)

That is, the value range of m is: - 15 4) m <-1 or 1 In the above two cases, the value range of m is - 15 4) m 15 4).

Note: (21 4 m2) represents the square root of (21 4 m2).

4m 2 means m squared multiplied by 4

15 4) denotes the square root of 15/4.

x^2-5/2)^2=m^2-21/4

There are two solid roots, so m 2-21 4>=0....1)x^2-5x-(m^2-1)=0

x=(5+or-root(25+4(m2-1))) 2 because of (1) so |a|+|b|= root number 4m 2 = 21m 2> = 15 4....2)

The m range is obtained from (1) and (2).

It's more complicated, so I won't answer, I'm sorry.

First of all, the discriminant formula of the quadratic equation δ b 2-4ac

Got: 25+4 (m 2-1).

21+4m^2

It is obtained by the root finding formula.

a=x1 5+ (21 4m2) 2 is obviously a>0

b=x2 Zen stool difference 5 (21 4m 2) 2 if, 5 (21 4m 2) then.

b 0, thus.

a│+│b│=5

The conditions are met. At this time.

5 (21 4m2), so.

The solution. 1≤m≤1

If, 5 (21 4m2) then.

b<0, m<-1 or m>1

Yu Kusong is. a + b = (21 4m 2) 6, solution.

M Heppi (15 4).

That is, the value range of m is: - 15 4) m

Or. 1. Based on the above two cases, the value range of m is as follows.

mNote: (21 4m2) denotes the square root of (21 4m2).

4m 2 means m squared multiplied by 4

15 4) denotes the square root of 15/4.

7a³-3（2a³b-a²b-a³）+6a³b-3a²b)-(10a³-3)

7a³-6a³b+3a²b+3a³+6a³b-3a²b-10a³+3

7+3-10)a³+(6-6)a³b+(3-3)a²b+3=0+0+0+3

3 The value of the polynomial has nothing to do with a or b, so her statement makes sense.

Yes Original Formula.

7a³+3a³-10a³)+6a³b+6a³b)+(3a²b-3a²b)+3

3 has nothing to do with the value of a, b.