Simplification: √ (x + 3) & # 178; + √ (X-2) & # 178; + √ X & # 178; - 10x + 25 (3)

Simplification: √ (x + 3) & # 178; + √ (X-2) & # 178; + √ X & # 178; - 10x + 25 (3)

30,x-5

|1-x | + √ 9-6x + X & # 178; (1 ≤ x ≤ 3) simplification

1-x≤0,3-x≥0
So the original formula = | 1-x | + √ (3-x) &# 178;
=|1-x|+|3-x|
=x-1+3-x
=2

If the maximum value of function f (x) = | x2 + x-t | in the interval [- 1,1] is 2, then the real number T=______ ．

∵ function f (x) = | x2 + x-t | = | (x + 12) 2-14-t |, in the interval [- 1, 1], the maximum value is 2, when 14 + T < 0, 1 + 1-T = 2 or 14 + T > 0, 14 + T = 2, t = 0 or T = 74, so the answer is: 0 or 74

The difference between a number and its reciprocal is 14 / 15

15
15-1/15=14 14/15

Let X1 and X2 be the two roots of the equation 2x ^ 2 + 4x-3 = 0
(x1) ^ 1 / 2 + (x2) ^ 1 / 2

According to the relationship between the root and coefficient of quadratic equation with one variable
x1+x2=-2
x1*x2=-3/2
X1) ^ 1 / 2 + (x2) ^ 1 / 2
=(x1^2+x2^2)/(x1*x2)^2
=[(x1+x2)^2-2x1*x2]/(x1*x2)^2
=[(-2)^2-2*(-3/2)]/(-3/2)^2
=28/9

Given the function f (x) = - x square + 2ex + M-1. G (x) = x + e square ratio x (x > 0)
Let g (x) - f (x) = 0 have two different real roots

Using the mean inequality, G (x) ≥ 2E. If and only if x = e, the equal sign is taken
It is noted that the axis of symmetry of F (x) is x = E. that is, f (x) and G (x) get the maximum and minimum at the same point
If G (x) = f (x) has two distinct real roots, it only needs f (x) max > G (x) min
The solution is m > - E & sup2; + 2E + 1
It's a little hard, but it's worked out

If the quadratic equation (M + 1) x2-2mx + M2-1 = 0 has two different sign roots, then the value range of M is ()
A. M ＜ 1b. M ＜ 1 and m ≠ - 1C. M ＞ 1D. - 1 ＜ m ＜ 1

Let two equations be x1, x2. According to the meaning of the problem, we get m + 1 ≠ 0, X1 + x2 = 2mm + 1 ＜ 0, x1 · x2 = M2 − 1m + 1 ＜ 0. We get m ＜ 1 and m ≠ - 1. Because x1 · x2 ＜ 0, △ 0, the range of M is m ＜ 1 and m ≠ - 1

The symmetry axis of a quadratic function is a straight line x = 1. The ordinate of the lowest point P on the image is - 8. The image passes through the point (- 2,10), and the X axis intersects a: B, and the Y axis intersects C

The problem is unclear

Solve the equation. 1.4x-1.6 × 5 = 1.8 & nbsp; & nbsp; & nbsp; & nbsp; 2x-52 = 14 & nbsp; & nbsp; & nbsp; & nbsp; x-15x = 310 & nbsp; & nbsp; & nbsp; 2.5: x = 7.5:12 & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; x45 = 5.829

（1）1.4x-1.6×5=1.8             1.4x-8=1.8           1.4x-8+8=1.8+8   &nbs...

If f (X & # 710; 6) = ㏒ 2x, find f (8)? X & # 710; 6 is the sixth power of X, and㏒ 2x is the logarithm based on 2

8 = 2 ^ 3 = (radical 2) ^ 6
F (8) = f (radical 2) ^ 6 = log2 (radical 2) = 1 / 2