X=2, then the value of this algebraic expression is 1 1, indicating that the value of this algebraic expression changes with the value of X.
(2) The math textbook page 105 says, "We call polynomial a2+2ab+b2 and a2-2ab+b2 completely flat". When factorizing with complete square formula, the key is to judge whether this polynomial is completely flat. Similarly, partial factorization of polynomials can solve the problem of the maximum (or minimum) value of algebraic values. For example, x2+2x+3 = (x2+2x+1)+2 = (x+ 1)2+2, because (x+1) 2 is non-negative.
(3) Find the maximum (or minimum) value of the algebraic expression -x2+ 14x+ 10 and write the corresponding value of x. 。
Answer:-x2+14x+10 =-(x2-14x+49)+59 = -(X-7)2+59 Because-(x-7) 2 is a non-positive number, this algebraic expression has a maximum value.
(4) Find the maximum (or minimum) value of the algebraic expression 2x2- 12x+ 1 and write the corresponding value of x. 。
Answer: 2x2-12x+1= 2 (x2-6x+9)-17 = 2 (X-3)2-17 Because (x-3) 2 is non-negative, this algebraic expression has a minimum value.
(5) It is known that y= the square of one-half x -3x- three-thirds, and the value of x varies between the numbers 1 ~ 4 (including 1 and 4). Find the change range of y at this time.
After work, give some points. . . .