Use the formula method to solve the following equation 1, the square of X + 8 = 4 times the root sign 2x, 2, the square of X + 5x = 3,3,2 / x the square of X + X + 3 = 6x-4,

Use the formula method to solve the following equation 1, the square of X + 8 = 4 times the root sign 2x, 2, the square of X + 5x = 3,3,2 / x the square of X + X + 3 = 6x-4,

1、x²-4√2x+8=0
(x-2√2)=0
x=2√2
2、-x²+5x=3
x²-5x+3=0
Δ=25-12=13>0
x=(5±√13)/2
3、1/2x²+x+3=6x-4
1/2x²-5x+7=0
x²-10x+14=0
Δ=100-56=44>0
x=(10±2√11)/2
x=5±√11

Find the value of root x + 1 - Radix 16-2x + the square of root minus x + root 4-5x

There is no negative number under the root sign,
The square of negative x ≥ 0
∴x=0
 root sign (x + 1) - root sign (16-2x) + root sign (square of negative x) + root sign (4-5x)
=Radical (0 + 1) - radical (16-0) + radical (0) + radical (4-0)
= 1 - 4 + 0 + 2
= -1

When x = - 2, the value of 5x? - 3x-1 under the radical of the algebraic expression is --, do not take it directly! There's another question: the minus two of one?

It is the most convenient method to substitute directly
√(5x²-3x-1)=√[5×(-2)²-3×(-2)-1]=√25=5
Any power of 1 is equal to 1, regardless of the exponent

Find the maximum value of y = radical (x? - 3x + 2) + radical (2 + 3x-x?)

Because [radical (x? - 3x + 2)] + [radical (2 + 3x-x?)]? = 4, let the root sign (x? - 3x + 2) = 2cosa, the radical sign (2 + 3x-x?) 2sina, the radical sign is greater than or equal to 0, so a ∈ [0, π / 2] so y = 2sina + 2cosa = 2 √ 2Sin (a + π / 4), so the maximum value of Y is 2 √ 2, and the minimum value of Y is 2 √ 2

Given that f (x) = 3x2-5x + 2, find f (- 2) , f (- a), f (a + 3), f (a) + F (3)

f(−
2)＝3×(−
2)2−5×(−
2)+2＝8+5
2，
f（-a）=3a2-5a+2，
f（a+3）=3（a+3）2-5（a+3）+2=3a2+5a+2，
f（a）+f（3）=3a2-5a+2+3×32-5×3+2=3a2-5a+16．

1 / 3x? - 4x-2x? + 5x + 2 / 3x? - x + 7, where x = radical 2, first merge similar items, and then calculate the value of the algebraic expression?

The original formula = (1 / 3-2 + 2 / 3) x 2 + (- 4 + 5-1) x + 7
=-x²+7
=-2+7
=5

Is 5x 2 + 2 radical 2x + 10 a quadratic equation of one variable? It's 5x? 2, 2x + 10 = 0

yes
Unary x
Quadratic square
It is estimated that you mainly see that the root sign L and the root sign 2x can simplify the half power of 2x, so the highest power is still the square power in front of the formula

The process of solving the problem is that the number of 2 roots is 5 x 2 y, and 4 parts are 25 x 3 y 2

2 pieces of 5x? Y, 4 pieces of 25X? Y
=
2X Radix 5Y 20XY Radix x
=
Root 5Y 10Y root x
=5Y 10Y root x * root 5Y
=2XY

Use factorization to solve the equation! 5x 2 + 1 = (2 radical 5) x

5x²－2√5x＋1=0
[√5x－1]²=0
√5x－1=0
x=√5/5

How to solve this equation by factorization?

2X? - (2 root sign 3-root 2) x-radical 6 = 0
1 - radical 3
2 root sign 2
(x-radical 3) (2x + Radix 2) = 0
X1 = radical 3
X2 = - radical 2 / 2
[questions are welcome]
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