Ask the question of the function, it is not difficult! Ask the math problem and solve it!

(1) If the function f(x)=sinx (x+2)(x+a) is an odd function, what is the value of the real number a?

Solution: f(x) is an odd function.

f(x)=-sinx/(x+2)(x+a)

f(-x)sin-x/(-x+2)(-x+a)

sinx (-x+2)(-x+a) "Because sinx=sin-x>

then (x+2)(x+a)=(-x+2)(-x+a).

Get a=-2 "Because we get x 2 + (2 + a) x + 2a = x 2-(2 + a)+2a, i.e. a = -2 >

2) Knowing that the function f(x) is an odd function, when x>0 and f(x)=lnx, what is the value of f(f(1 e 2)))?

Solution: Let x 0, then -x 0

f(-x)=ln-x=-f(x)

then when x 0, f(x)=-ln-x

Function f(x) = lnx , x>0

ln-x ,x<0

then f(f(1 e 2)) = f(lne -2).

f(-2)-ln2

The <> part is easy to understand and does not need to be written during the formal answering process

(1)f（x） ＋f（－x） ＝0

Since sin x = -sin(0-x).

So bring in the calculations:

x+2)(x+a) = (-x+2)(-x+a) so a = -2

2)f(1/e^2) =ln(1/e^2) = -2f(f(1/e^2))=f(-2) = -f(2) = -ln2

Solution: f(x) is an even function defined on r, when 0 x 1, f(x)=x2, when -1 x 0, 0 -x 1, f(-x)=(-x)2=x2=f(x), and f(x+2)=f(x), f(x) is a function with period 2, and the image of the line y=x+a and the function y=f(x) has two different common points in [0,2], and the image is as follows:

When a=0, the line y=x+a becomes the line l1, and the equation is: y=x, and it is obvious that the image of l1 and the function y=f(x) has two different common points in [0,2];

When a≠0, the image of the line y=x+a and the function y=f(x) has exactly two different common points in [0,2], and it can be seen from the graph that the line y=x+a is tangent to the function y=f(x), and the abscissa of the tangent point is x0 [0,1].

by y=x+a

y=x2 yields: x2-x-a=0, and =1+4a=0 yields a=-

14, at this point, x0=x=

In summary, a=-

14 or 0

(1) Since it is an odd function of y=sinx, as long as g(x)=(x+2)(x+a) is an even function, so that g(x)-g(-x)=0 is constant, the solution is a= 2, and when a= 2 is tested, f(x) is an odd function.

2）f(f(1/e^2))=f(ln1/e^2)=f(-2)=-f(2)=－ln2.

Let the middle even number be x, then.

The three sides of the triangle are.

x-2,x,x+2

and x+2 is its hypotenuse.

By the Pythagorean theorem.

x+2)^2=(x-2)^2+x^2

Get x 2-8x=0

And x is not equal to 0

x=8, so its three sides are 6, 8, 10

The area is 6*8 2=24

Let the smallest side be x, then the other two sides are x+2 and x+4; According to the Pythagorean law equation, this estimate you will, that is.

x^2+(x+2)^2=(x+4)^2;

If the three sides are x=6, then the remaining two sides are 8 and 10.

Its area is 24.

I hope it will help you, and I wish you progress in your studies and early success. Don't forget to give me a good review. Thank you.

Let the length of the right-angled side be x, then:

x^2+(x-2)^2=(x+2)^2

Solution: x=8 (x=0, rounded).

The three sides are long

Area = 6 * 8 2 = 24

You know the formula for solving binary equations.

In this formula.

The quadratic coefficient a=2 the coefficient of the primary term b=k constant c=-1b 2-4ac is called the discriminant formula of the root.

If b 2-4ac 0 then the original equation has two unequal real solutions, if b 2-4ac = 0 then the original equation has two equal real solutions, and if b 2-4ac 0 then the original equation has no real solutions in this equation.

b²-4ac=k²+8

k 0 so k +8 0 so the original equation has two unequal solutions to real numbers.

It proves that there is a mathematical symbol that can't be typed, and it doesn't matter.

It is the special equation b -4ac=k -4 2 (-1)=k +8

Because k 0

So k +8 0

i.e. b -4ac 0

So the equation has two unequal real roots.

By the way, this symbol is squared.

Discriminant = k 2 + 8>0, so the equation has two unequal real roots.

=b 2-4ac=k 2-4 2 (-1)=k 2+8 8 0 So the equation has 2 unequal real roots. Proven.

If the circumference is 600 meters, and the length is y meters, then the width is 600 2-y, which is y*(600 2-y)=20000

300y-y^2-20000=0

y^2-300y+20000=0

y-150)^2-2500=0

Find y=200 meters.

That is, an increase of 200-100 = 100 meters.

Ahem, first of all, your question is 8 x&sup8;+kx-8=1 Right, if yes, I'll start answering Proof There's a mathematical symbol that can't be typed It doesn't matter It's a special equation because k&su

Let the length be y meters, then the width is 600 2-y

y*（600/2-y）=20000

300y-y^2-20000=0

y^2-300y+20000=0

y-150)^2-2500=0

then y = 200 meters.

So an increase of 200-100 = 100 meters.

Let the two be x1 and x2 respectively, and set x1 2

x1+x2=1

So x2 0 and |x1|=|x2|+1

k=-x1x2

x1=2, x2=-1

x1x2=-2

So k 2

Method 1 (Requested by the landlord!) ）

Let the two roots of the equation be x1 and x2, and according to Veda's theorem, x1 x2=-k; x1+x2=1 (may wish to let x2 be the root greater than 2, x1 is the root less than 2) x2>2, 1-x1>2 to get x1<-1So x1·x2=-k, x1·x2 is a subtraction function, and the minimum value is less than -2, and -x1·x2=k, so k (-2).

Method 2 (with the help of the zero point according to the image).

The equation x 2-x-k=0 is the value of the function f(x)=x 2-x-k, f(x)=0.

The image opens upward, you can do the problem without writing the parentheses) There is a root greater than 2, and the other root is less than 2, only f(2)<0 can satisfy the question f(2)<0 to get k (-2).

The second way to solve this problem is to send it through, which is simpler!

x1+x2=1,x1>2, i.e. 1-x2>2,x2<-1x2<2 takes x2<-1Because x1>2 so x1x2=-k<-2, so k>2

Solution: If ax 2+bx+c=0 (a!=0) with two unequal real roots, then discriminant b 2-4ac>0

By title: 2k-1) 2-4(k-1)*4k>012k 2+12k+1>0

3-2*sqr(3))/6

The first floor is the correct solution, because k-1 is the denominator in the two roots, so k cannot be equal to 1

Just judge according to the discriminative condition of the root, note that k can't be 1 at the end, that's where it's easy to make mistakes.

2k-1) 2-4(k-1)(4k)>0 and k cannot be 1

This is good to say, according to the parabola (I don't know if you have learned), this quadratic acre carrying is a parabola, it is open upward (U-shaped), then as long as its vertex (that is, the minimum value is greater than 0), then it is greater than 0 for any real number, m 2 + 14m + 65 The axis of symmetry is x=-b 2a=-7, and the -7 substitution is calculated to calculate its minimum knowing volt value is 16, that is, the minimum value of this formula is 16, then of course it is greater than 0!

Got it! Correct, please give the best, thank you for your cooperation!

m^2+14m+65=(m+7)^2+16

Because the former blind orange is the number of square dates that are completely flattened, greater than or equal to 0, and then add 16 to the side, it must be greater than 0

△=4a^2-4(b-c)(b-c)

4a^2-4(b-c)^2

4(a+b-c)(a-b+c)

Because abc is the three sides of the triangle, the sum of the two sides of the triangle is greater than the third side, so a+b-c>0, a+c-b>0

So >0

So the equation (b-c) x 2-2ax + b-c=0 has two different real roots.

Directly use the discriminant formula.

4a -4(b-c)(b-c)=4(a+b-c)(a-b+c) is known according to the fact that the sum of the two sides of the triangle is greater than the third side.

a+b-c＞0，a-b+c＞0

i.e. 0 The equation with respect to x (b-c) x 2-2ax + b-c = 0 (b is not equal to c) has two unequal real roots.

=4a -4(b-c) =4(a+b-c)(a-b+c) Because the sum of any two sides of the triangle is greater than the third side, the above equation is greater than 0 so there are two roots, set to x1, x2

x1x2 = 4(b-c) 0, x1+x2=a (b-c), which may be positive or negative.

So the equation has two roots, both positive and negative.