Let a and B satisfy a 2-8a + 6 = 0 and 6B 2-8b + 1 = 0, and find the value of AB + 1ab

Let a and B satisfy a 2-8a + 6 = 0 and 6B 2-8b + 1 = 0, and find the value of AB + 1ab

Because 6b2-8b + 1 = 0, then B ≠ 0, then (1b) 2 − 8 × 1b + 6 = 0, when a ≠ 1b, then a, 1B are the two roots of the equation x2-8x + 6 = 0, let X1 = a, X2 = 1b, then X1 + x2 = 8, x1x2 = 6, so AB + 1ab = x1x2 + x2x1 = (x1 + x2) 2 − 2x1x2x1x2 = 64 − 126 = 263, when a = 1b, that is, AB

1. Given that real numbers a and B satisfy 2a2-8a + 3 = 0, 3b2-8b + 2 = 0, and ab ≠ 1, find the value of A2 + 1 / B2
2. Discuss the root of the equation (m-2) x2 + (2m-1) x + m-2 = 0

Given that real numbers a and B satisfy 2a2-8a + 3 = 0, 3b2-8b + 2 = 0, and ab ≠ 1, find the value of A2 + 1 / B2
3b ^ 2-8b + 2 = 0, divide both sides by B ^ 2
3-8/b+2/b^2=0
That is, 2 (1 / b ^ 2) - 8 * 1 / B + 3 = 0
Then it can be seen that a and 1 / b are two unequal real roots of the equation 2x ^ 2-8x + 3 = 0. (because ab ≠ 1, then a ≠ 1 / b)
a+1/b=4
a*1/b=3/2
a^2+1/b^2=(a+1/b)^2-2a*1/b=16-2*3/2=13
Let's ask the second question again. There's no time

If real numbers a and B satisfy ab ≠ 0, and (a ^ 2 + B ^ 2) ^ 3 = (a ^ 3 + B ^ 3) ^ 2 + 8A ^ 3B ^ 3, find the value of a / B + B / A

10/3
The method is to use the formula to open the brackets, then merge the similar items, and then place a ^ 3B ^ 3 on both sides

Find the minimum value of the second power of a + 8A + 25,

a^2+8a+25
The symmetry axis of the function is - B / 2A = - 4
Substitute - 4 to get the minimum value: 16-32 + 25 = 9

When a, B what value, the quadratic power of 4A + the quadratic power of B - 4A + 6B + 10 take the minimum, and find out the minimum

4a²＋b²－4a＋6b＋10
＝ ﹙4a²－4a＋1﹚＋﹙b²＋6b＋9﹚
＝﹙2a－1﹚²＋﹙b＋3﹚²
When 2a-1 = 0, B + 3 = 0
That is: a = 1 / 2, B = - 3
The minimum value of this algebraic expression is 0

What is the minimum value of a + B = 2,3 to the power of a + to the power of B
What is the minimum value of a + B = 2, 3 to the power of a + 3 to the power of B

Mean inequality, the a power of 3 + the B power of 3 is greater than or equal to the a + B power of 3 under the root of 2 * = 6
When a = b = 1

The minimum value of a + B = 2,3 to the power of a plus 3 to the power of B
It's also mean inequality

Yes
3^a+3^b>=2√(^a*3^b)=2√3^(a+b)=6
So the minimum value is 6

13 out of 8 is 1 and 8

Fill in the blanks according to the rule: 14 () times 2 () 6 equals () 1470

The three numbers are 5.8.4
First of all, look at the first one. Multiply 6 bits to get a multiple of 10 (the last one is 0), so it's only 5. Then the first number is 145
We can set the number in the middle as X, that is, 145 * 2x6 = y1470,
145*（200+10x+6）=10000y+1470
29870+1450x=10000y+1470
Now let's talk about the value of 1450 X
First of all, the bits of the three numbers are all 0, so no problem
And then there are ten, seven, five, seven
In order to guarantee the validity of the transformation, 5x must be a multiple of 10. Only in this way can the tens of the second number be 0, 7 + 0 = 7, because x is less than 10
So x can be equal to 2.6.8
Substitute three numbers, and finally only x = 8 makes it true
145*286=41470

Fill in the circle with a greater than, less than, or equal sign 6 and circle 6 = 0

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