A 120cm long wire is divided into two parts, each part is bent into a square. What is the sum of their areas? What's the area and minimum of them?

Let the iron wire be divided into two parts xcm and (120-x) cm, and the sum of the areas is y. The equation shows that y = (x4) 2 + (120 − x4) 2 = 18 (X-60) 2 + 450 ∥ the sum of their areas is 18 (X-60) 2 + 450, and the minimum value is 450cm2

A 120cm long wire is divided into two parts, each part is bent into a square. What is the sum of their areas? What's the area and minimum of them?

When x = - 1 / 2, the quadratic function y = (a + b) x + 2cx - (a-b) has a minimum value of - B / 2. Try to determine the shape of △ ABC with ABC as the edge

When x = - is brought into the function equation, there are: (a + b) / 4-C + A-B = - B / 2, that is, 5a-b-4c = 0. (1) because in the quadratic function y = (a + b) x + 2cx + (a-b), the quadratic term (a + b) > 0, then the opening of the function is upward, then the intersection of the symmetry axis of the function and the function is the minimum, that is, when x = - 2C / 2 (a + b) = -, That is, a + B = 2C. (2) the joint solution (1) and (2) obtains a = B, where the function value is: (4 (a + b) (a-b) - (2C)) / 4 (a + b) = - B / 2, and brings a = B into a = C, that is, a = b = C, and the triangle is an equilateral triangle
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Let ABC be the length of three sides of △ ABC, and the minimum value of quadratic function y = (a-b / 2) x-cx-a-b / 2 is - 8 / 5B when x = 1. Judge the shape of △ ABC

The quadratic function can be expressed as y = (a-b / 2) (X-B / 2) (x-2-b / 2) (X-1-1) (X-1-1) (x-1) - 8B / 5 quadraticfunction can be expressed as y = (a-b / 2) (X-B / 2) (X-B / 2) (X-B / 2) (X-B / 2) () (X-B / 2) (X-B / 2) x-cx-a-b-a-8 / 5B \ \ \ \ \ \\\\\\\\\\\\\\\\\\\\\\a + C = B △ ABC is a right triangle

What is the minimum side length of a triangle when a / b = (x 2-2 / b) a / C = 8

y`=2(a-b/2)x-c=0
x=1
2a-b-c=0
y=a-b/2-c-a-b/2=-b-c=-8/5b
c=3/5b
2a=b+c=8/5b
a=4/5b
b=5m a=4m c=3m
a^2+c^2=b^2
It's a right triangle

If the ABC in the quadratic function y = (a-b) x ^ 2 + 2cx - (a + b) are the lengths of the three sides of the triangle ABC respectively, then when there is only one intersection point between the quadratic function and the X axis,
What is the shape of the triangle ABC?

Right triangle

Let f (x) = 1 x-ax and f (1) = - 1. (1) find the analytic expression of F (x) and judge its parity; (2) prove that f (x) is a monotone decreasing function in the interval (0, + ∞)

(1) ∵ f (1) = - 1. ∵ 1-A = - 1 ∵ a = 2 ∵ f (x) = 1x-2x ∵ f (- x) = 1 − x − 2 × & nbsp; (− x) = - 1x + 2x ∵ f (- x) = - f (x), so the function is odd. (2) let 0 ＜ x1 ＜ X2, then f (x1) - f (x2) = 1x1 − 2x1 − (1x2 − 2x2) & nbsp; = (x2 − x1) (1 + 2 & nbsp; & nbsp; x1x2) & nbsp; & nbsp; & nbsp; The function f (x) is a decreasing function in the interval (0, + ∞)

Given the function f (x) = [A / (a 2-1)] (ax-a-x) (a > 1) (1) judge the parity of F (x) and prove that (2) judge the monotonicity of F (x) and prove that (3) when x belongs to [- 1.1], f (x) > = m is constant, find the range of M and get the detailed explanation

(1) F (- x) is not equal to f (x) or - f (x), not odd or even. (2) the derivative of F '(x) is always greater than zero, increasing monotonically

A 120cm long wire is divided into two parts, each part is bent into a square. What is the sum of their areas? What's the area and minimum of them?