Solution: x? -2x？ y-xy？ +2y？ =x^2(x-2y)-y^2(x-2y)=(x^2-y^2)(x-2y)=0
∵x>y>0,∴ x^2-y^2>0
∴ x-2y=0
∴xz-2yz+ 1 = z(x-2y)+ 1 = 0+ 1 = 1
2. use equation x? -3x- 1=0。 What is a quadratic equation with two roots squared?
Solution: let equation x? -3x- 1=0 is X 1 and X2,
Then there are: x 1+x2 =-b/a = 3, x 1 * x2 = c/a =- 1.
Let's assume the equation x? The quadratic equation of the square of two roots of -3x- 1=0 is ax 2+bx+c = 0.
Yes: x 1 2+x2 2 =-b/a, x12 * x22 = c/a.
* x 1^2+x2^2=(x 1+x2)^2-2x 1*x2=3*3+2= 1 1
X 1^2*X2^2= 1
∴ -B/A= 1 1，C/A= 1
Let A= 1, then B=- 1 1, and C= 1.
∴ and equation x? -3x- 1=0。 The quadratic equation of one variable with the square of two roots as the root is:
x^2- 1 1x+ 1=0
3. solve the equation: x? +8x+ x under the root symbol? +8x= 12
Solution: let x 2+8x = y.
Original formula =y+√y= 12.
√y= 12-y
Square both sides at the same time: y = y 2-24y+144.
Solve y,
After solving x 2+8x = y, you can