When k is a value, the equation kx2-x + 1 = 0 has two unequal real roots? When k is a value, the equation kx2-x + 1 = 0 has no real roots?

When k is a value, the equation kx2-x + 1 = 0 has two unequal real roots? When k is a value, the equation kx2-x + 1 = 0 has no real roots?

1、
The discriminant is greater than 0
1-4k>0
k

It is known that the equation kx2-2 (K + 1) x + k-1 = 0 has two unequal real roots, then the value range of K is___ ．

∵ a = k, B = - 2 (K + 1), C = k-1, △ = b2-4ac = 12K + 4 ＞ 0, that is to say, the K ＞ - 13 equation has two unequal real roots, then the quadratic coefficient is not zero, K ≠ 0. Therefore, the answer is k ＞ - 13 and K ≠ 0

Three fourths of the number a is equal to the number B. the number a is three fourths, and the number B is?

The second number is
3 / 4 × 3 / 4 = 9 / 16

Let AX = have a solution, where a is a matrix M times n. It is proved that AX = B has a unique solution if and only if the product of a transpose and a is positive definite

Because AX = B has a solution, R (a) = R (a, b)
So at this point
Ax = B has unique solution
r(A)=n
Ax = 0 has only zero solution
Ax ≠ 0 when x ≠ 0
When x ≠ 0 (AX) ^ t (AX) > 0 (a is a real matrix)
When x ≠ 0, x ^ t (a ^ TA) x > 0
A ^ TA is positive definite

A total of 585 parts were produced by Party A, Party B and Party C. the number of parts produced by Party A is 4 / 5 of that of Party B, and the number of parts produced by Party B is 8 / 9 of that of Party C,
How many parts each of a, B and C can produce

C: 585 ÷ (1 + 8 / 9 + 8 / 9 × 4 / 5) = 225
B: 225 × 8 / 9 = 200
A: 200 × 4 / 5 = 160

How much is (7x-3y) - (10y-5x)?

First floor that's wrong!
（7x-3y）-（10y-5x）
Remove bracket = 7x-3y-10y + 5x
Merge congeners = 12x-13y

A warehouse has 110 tons of grain and B warehouse has 70 tons. How many tons can be taken out from a warehouse and put into B warehouse to make the grain tonnage ratio of a warehouse to B warehouse 5:13?

Now the ratio is 100:70 = 11:7, so the ratio of 11-5 = 6, 110 △ 5 = 22, 6 times 22 = 132 tons is 5:1

#Open sesame door 4 / 7x-27 / 11 = 0.125-1 / 28x

From the original formula, it is concluded that:
4/7X+1/28X=1/8+27/11
17/28X=227/88
X=227*28/88*17
X=1589/374

It's a simple operation
10×11÷1＋11×12÷1＋12×13÷1＋13×14÷1＋14×15÷1
The equal sign should be under the formula

10×11÷1＋11×12÷1＋12×13÷1＋13×14÷1＋14×15÷1
=10*11+11*12+12*13+13*14+14*15
=110+12*(11+13)+14*(13+15)
=110+12*12*2+14*14*2
=110+2*(144+196)
=110+2*340
=110+680
=790
Or:
Let a = 10, then the original formula = a (a + 1) + (a + 1) (a + 2) + (a + 2) (a + 3) + (a + 3) (a + 4) + (a + 4) (a + 5)
=(a+1)(a+a+2)+(a+3)(a+2+a+4)+(a+4)(a+5)
=2*(a+1)(a+1)+2*(a+3)(a+3)+(a+4)(a+5)
=2a^2+4a+2 +2a^2+12a+18+a^2+9a+20
=5a^2+25a+40
=500+250+40
=790

Let the common ratio Q of the equal ratio sequence {an} be 1 / 2 and the sum of the first n terms be Sn, then S4 / A4 =?

S4=a1(1-1/(2^4)/(1-1/2)
=15a1/8
a4=a1/8
S4/a4=15