Complete square formula: a 2; 2ab+b^2； = (a b) 2; ;

Note: Polynomials that can be decomposed by the complete square formula must be trinomial, two of which can be written as the sum of squares of two numbers (or formulas), and the other is twice the product of these two numbers (or formulas).

Cubic sum formula: A3; +b^3； =(a+b)(a^2； -ab+b^2； );

Cubic difference formula: A3; -b^3； =(a-b)(a^2； +ab+b^2； );

Complete cubic formula: A3; 3a^2； b+3ab^2； b^3； = (a b) 3; .

Other formulas: (1) a3; +b^3； +c^3； +3abc=(a+b+c)(a^2； +b^2； +c^2； -ab-bc-ca)

For example: a 2；; +4ab+4b^2； =(a+2b)^

Knowledge points in junior high school mathematics formula method II. Change the quadratic equation of one variable into the general form of ax2+bx+c, and then substitute the values of various coefficients A, B and C into the formula to find the root of the equation.

Formula method

Formula: x = [-b √ (B2-4ac)]/2a.

When δ = B2-4ac >; 0, the root formula is x 1 = [-b+√ (B2-4ac)]/2a, x2 = [-b-√ (B24ac)]/2a (two unequal real roots).

When δ = B2-4ac = 0, the formula for finding the root is x 1=x2=-b/2a (two equal real roots).

When δ = B2-4ac

Example 3. Solving Equation 2x2-8x=-5 by Formula Method

Solution: Change the equation into a general form: 2x2-8x+5=0.

∴a=2，b=-8，c=5

B2-4ac =(-8)2-4×2×5 = 64-40 = 24 & gt； 0

∴x= (4 √6)/2

∴ The solution of the original equation is x? =(4+√6)/2，x？ =(4-√6)/2.

What we don't know is that two complex roots are understood as having no real roots in junior high school mathematics learning.