When k is a value, the fractional equation x + 1 / K plus X-1 / 1 = x minus 1 / 1 has no solution as soon as possible

When k is a value, the fractional equation x + 1 / K plus X-1 / 1 = x minus 1 / 1 has no solution as soon as possible

It is concluded that (K + 1) x = k can only produce increasing root 1 or - 1 if there is no solution to the original equation or K = - 1 / 2 or - 1 if there is no solution to the above equation
If the fraction equation X-1 x-k minus x-3 equals 1 with no solution, find the value of K
(x－k)/(x－1)－3/x＝1
If we remove the denominator and sort it out, we get (K + 2) x = 3
So x = 3 / (K + 2)
Because the equation has no solution, x = 0 or 1
When x = 0, K has no solution,
When x = 1, 3 / (K + 2) = 1, k = 1
(x－k)/(x－1)－3/x＝1
If we remove the denominator and sort it out, we get (K + 2) x = 3
So x = 3 / (K + 2)
Because the equation has no solution, so x has no meaning, then k = - 2
K = 1 or - 2
If 1y equals 1, 2Y equals 1x2, 3Y equals 1x2x3, 5Y equals what? (4Y plus 8y) divided by 5Y equals what
5y=1×2×3×4×5
(4y+8y)÷5y=(1×2×3×4+1×2×3×4×5×6×7×8）/（1×2×3×4×5）
=（1+5×6×7×8）/5
=1681/5
Your y is the factorial
1！ ＝1
2！ ＝2×1
3！ ＝3×2×1
1、5！ ＝5×4×3×2×1＝120
2、（4！ +8！） ÷5！
＝（4！ ÷5！） +（8！ ÷5！）
＝（4×3×2×1）÷（5×4×3×2×1）+（8×7×6×5×4×3×2×1×）÷（5×4×3×2×1）
＝1/5 + 8×7×6
= 336 and 1 / 5
This kind of problem is regular, and there are many methods. The more old-fashioned way is to look at the rule, and multiply and add one by one according to the requirements, and divide by 5Y, which will be very complicated. You can simplify the required formula: (4Y plus 8y) divide by 5Y equals 4Y / 5Y + 8y / 5Y, so it's easy to calculate ~ they are the numbers from 1 to y, you can look at the rule, in this way, you can simplify the equation: 4Y / 5Y +8y / 5Y, can be substituted into the specific number or not, 4Y / 5Y is reduced to 1 / 5 equal to 0.2. And 8y / 5Y is reduced to 6 * 7 * 8 and so on
This kind of problem is regular, and there are many methods. The more old-fashioned way is to look at the rule, and multiply and add one by one according to the requirements, and divide by 5Y, which will be very complicated. You can simplify the required formula: (4Y plus 8y) divide by 5Y equals 4Y / 5Y + 8y / 5Y, so it's easy to calculate ~ they are the numbers from 1 to y, you can look at the rule, in this way, you can simplify the equation: 4Y / 5Y +8y / 5Y, can be substituted into the specific number or not, 4Y / 5Y is reduced to 1 / 5 equal to 0.2. And 8y / 5Y is reduced to 6 * 7 * 8, which is equal to 336. The final solution is that 0.2 plus 336 equals 336.2. You can also use sequence and hierarchy. If the number is large, use sequence. Otherwise, it's hard to calculate
Let p be the moving point on the straight line 3x + 4Y + 8 = 0, PA and Pb be the two tangent lines of the circle m, and a and B be the tangent points, then the minimum area of the quadrilateral pamb is obtained
The area of quadrilateral PAM is twice that of right triangle PAM; the area of right triangle PAM is (1 / 2) × PA × am; because am = R is a fixed value, the area of triangle PAM can be minimized as long as PA is minimized; that is to say, as long as PM is minimized, the area of triangle PAM can be minimized, that is, four
It is proved by collocation that the value of the algebraic formula 5x & # 178; - x + 2 is not less than 39 / 20
5x²-x+2
=5(X^2-1/5X+1/100)+2-5×1/100
=5(X-1/10)^2+39/20
∵5(X-1/10)^2≥0,
The original formula ≥ 39 / 20
That is, the original formula is not less than 39 / 20
Given that X and y satisfy (2x + 3y-1) square + | x-2y + 2 | = 0, find the square root of 4Y of X-5
The square of (2x + 3y-1) + | x-2y + 2 | = 0
2X + 3y-1 = 0, and x-2y + 2 = 0
x=-4/7,y=5/7
4/5y = 4/5*5/7 = 4/7
Square root of 4 / 5 y ± √ (4 / 7) = ± 2 √ 7 / 7
The square root of X - 5 / 4Y = - 4 / 7 ± 2 √ 7 / 7 = (- 4-2 √ 7) / 7, or (- 4 + 2 √ 7) / 7
Given the quadratic function y = AX2 + BX + C, when x = - 1, there is a minimum value of - 4, and the length of the line segment of the image on the x-axis is 4, the analytic expression of the function is obtained
∵ the symmetry axis of the parabola is x = - 1, the length of the line segment on the x-axis is 4, the coordinates of the intersection of the parabola and the x-axis are (- 3,0), (1,0), let the analytical formula of the parabola be y = a (x + 3) (x-1), and substitute the vertex coordinates (- 1, - 4) to get a (- 1 + 3) (- 1-1) = - 4, and the solution is a = 1, ∵ the analytical formula of the parabola is y = (x + 3) (x-1), that is y = x2 + 2x-3
Formula method to solve 3Y ^ 2-2y = 2Y + 3
That is, 3Y & # 178; - 4y-3 = 0
So a = 3, B = - 4, C = - 3
Then △ = B & # 178; - 4ac = 16 + 36 = 52 = (2 √ 13) &# 178;
So y = (4 ± 2 √ 13) / 6
y1=(2-√13)/3,y2=(2+√13)/3
It is known that P is the moving point on the straight line 3x + 4Y + 8 = 0, PA and Pb are the two tangent lines of the circle x2 + y2-2x-2y + 1 = 0, a and B are the tangent points, C is the center of the circle, then the minimum area of PACB of quadrilateral is______ .
∵ the equation of circle is: x2 + y2-2x-2y + 1 = 0 ∵ center C (1,1), radius R is: 1. According to the meaning, if the area of quadrilateral is the smallest, when the distance between the center of circle and point P is the smallest, and the distance between the center of circle and straight line is the distance between the center of circle and straight line, the tangent length PA, Pb is d = 3 ∵ PA | = | Pb | = D2 − R2 = 22 ∵ spacb = 2 × 12 | PA | r = 22, so the answer is: 22
Try to explain: when x and y are arbitrary real numbers, the value of the algebraic formula x + y + 2x-8y + 18 is not less than 1
（x+1)^2+(y-4)^2+1≥1