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Math in Grade Three and Grade Three.
1. known x? -2x? y-xy? +2y? =0, x > y > 0, simplified as xz-2yz+ 1.

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