(6) Known, √ (3-x) &# 178; = x-3, √ (X-5) &# 178; = 5-x, simplified: √ 25-10x + X & # 178; + √ X & # 178; - 6x + 9

(6) Known, √ (3-x) &# 178; = x-3, √ (X-5) &# 178; = 5-x, simplified: √ 25-10x + X & # 178; + √ X & # 178; - 6x + 9

∵√(3-x)²=x-3
∴x-3≥0,x≥3
∵√(x-5)²=5-x
∴5-x≥0,x≤5
∴3≤x≤5
√(25-10x+x²)+√(x²-6x+9)
=√(5-x)²+√(x-3)²
=|5-x|+|x-3|
=5-x+x-3
=2

Simplify √ X & # 178; + 6x + 9 + √ X & # 178; - 4x + 4 - √ X & # 178; - 10x + 25

The first step is the formula. It's easier, X2 + 6x + 9 = (x + 3) square, x2-4x + 4 = (X-2) square, x2-10x + 25 = (X-5) square
The second step is to discuss the classification, because the problem of plus and minus sign should be considered in the root opening

When - 3 ≤ x ≤ 2, simplify | X-2 | + √ (x + 3) & # 178; + √ X & # 178; - 10x + 25=

x-2≤0
x+3≥0
x-5

It is known that the square of a with y = (3a + 1) x-a-3 is an inverse proportional function, and the value of a is obtained

The coefficient of X term is not equal to 0 and the exponent is - 1
3a+1≠0 a≠-1/3
a²-a-3=-1
a²-a-2=0
(a-2)(a+1)=0
A = 2 or a = - 1

Let the inequality mx2-2x-m + 1 < 0 hold for all the values of M satisfying | m | ≤ 2, and find the value range of X

Let f (m) = m (x2-1) - 2x + 1, and the condition f (m) < 0 holds for all m values satisfying | m | ≤ 2, then f (- 2) < 0 and f (2) < 0 are required. Solve the inequality system − 2x2 − 2x + 3 ＜ 02x2 − 2x − 1 ＜ 0, and the solution − 1 + 72 ＜ x ＜ 1 + 32 is − 1 + 72 ＜ x ＜ 1 + 32

(a-3)²-a(a-2)

=a²-6a+9-(a²-2a)
=a²-6a+9-a²+2a
=-4a+9

Are the areas of the two parallelograms in the figure below equal? The bottom is 2.5cm, the height is 1.4cm. What are their respective areas

Two parallelograms with equal base and height have equal area
S=ah
=2.5 times 1.4
=3.5

16 / 51 × 1 / 6 △ 8 / 9

16 / 5 × 1 / 6 ／ 8 / 9
=8/15×9/8
=3/5

The tangent equation of curve y = 2x ^ 2-1 at point P (- 3,17) is

Seeking derivative
y’=4x
Substituting x = - 3 into the derivative equation
We get y = - 12
So the tangent equation
y=-12（x+3）+17
y=-12x-19

-7x（-3）x（-0.5）+（-12）x（-2.6）=

-7x（-3）x（-0.5）+（-12）x（-2.6）
=21x(-0.5)+31.2
=-10.5+31.2
=20.7