Given sin (x - π / 4) = 3 / 5, ∈ (π / 4, π / 2), find the value of cos2x? As the title Is x ∈ (π / 4, π / 2)

Given sin (x - π / 4) = 3 / 5, ∈ (π / 4, π / 2), find the value of cos2x? As the title Is x ∈ (π / 4, π / 2)

Sin (π / 6) = 3 / 5, so x = π / 6 + π / 4 = 5 π / 12
2x=5π/6
cos(2x)=cos(5π/6)=-cos(π-5π/6)=-cos(π/6)=-4/5
It's not easy to type,

If the function y = x2-2x + 3 has a maximum value of 3 and a minimum value of 2 on the interval [0, M], then the value range of M is () A. [1，∞） B. [0，2] C. （-∞，2] D. [1，2]

The symmetrical axis of parabola is x=1, and the opening is upward
/ / 0 is on the left side of the axis of symmetry
∵ the image on the left side of the axis of symmetry decreases monotonically
The maximum value is 3 when x = 0 on the left side of the symmetry axis
When x = 1, y = 2
The value range of M must be greater than or equal to 1
∵ the image of parabola is symmetric about x = 1
/ / M must be ≤ 2
Therefore, D

Given that the maximum value of the function y = (AX + b) / (x ^ 2 + 1) is 4 and the minimum value is - 1, find the value of real number A.B X ^ 2 is the square of X

y=（ax+b)/(x^2+1)
ax+b=yx^2+y
yx^2-ax+y-b=0
The equation of X has a real number solution, and the discriminant is greater than or equal to zero
a^2-4y(y-b)>=0
-4y^2+4by+a^2>=0
y^2-by-a^2/4

Let x + y = 5, xy = minus 3, find the value of the algebraic formula (2x minus 3Y minus 2XY) minus (x minus 4Y + XY)

x+y=5
xy=-3
(2x-3y-2xy)-(x-4y+xy)
=2x-3y-2xy-x+4y-xy
=x+y-3xy
=5-3×(-3)
=5+9
=14

(2x-3y-2xy) - (x-4y + 7xy), where x + y = 5, xy = - 3, there should be a specific calculation process!

（2X-3Y-2XY）-（X-4Y+7XY）,
=2x-3y-2xy-x+4y-7xy
=x+y-9xy
=5-9*(-3)
=32

Given x 2 + X + 1 = 0, find the value of 4x? + 3x? + 2x + 1

x²+x+1=0
4x³+3x²+3x+1
=4x^3+4x^2+4x-x^2-x+1 4x^3+4x^2+4x=4x(x²+x+1)=0
=-x^2-x+1 x+1=-x^2
=x+1-x+1
=2

Given x ^ 2-2x-3 = 0, find the value of ① x ^ 2 + (1 / x ^ 2) ② x ^ 4 + (1 / x ^ 4) Given x ^ 2-2x-3 = 0, find the value of ① x ^ 2 + (1 / x ^ 2) ② x ^ 4 + (1 / x ^ 4)

(x+1)(x-3)=0
x=-1;x=3
x^2+(1\x^2)=(-1)^2+{1\(-1)^2}=2;3^2+(1\3^2)=9+1\9=82\9
x^4+(1\x^4)=(-1)^4+{1\(-1)^4}=2;3^4+(1\3^4)=81+1\81=6562\81

Given that the value of the square of the algebraic expression 2x + 5x + C is 14 when x = 2, find the value of the algebraic expression when x = - 2

When x = 2, the square of the algebraic expression 2x + 5x + C is 14
∴8+10+c=14
∴c=-4
When x = - 2
Original formula = square of 2x + 5x-4
=8-10-4
=-6

Given x 2 + X + 1 = 0, find the value of the fourth power of X + 2x 3 - 2x + 2005

The original formula = - 1 × x? - 2x + 2005 = 1 + 2005 = 2006

Given the square of X + 2x-1 = 0, try to find the value of the square of X + 1 / 1 of X

Given that the square of X + 2x-1 = 0, the value of square of X + 1 / 1 of x = 6