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2 years ago

If x2+1/x2=18, find the value of x3−1/x3

Mathematics

2 answers:

Elden [556K]2 years ago

7 0

Answer:

There are 2 answers : 76 or -76

Step-by-step explanation:

$x^2+\dfrac{1}{x^2} =18\\\\(x-\dfrac{1}{x} )^2=x^2+\dfrac{1}{x^2} -2=18-2=16\\\\x-\dfrac{1}{x}=4\ or\ x-\dfrac{1}{x}-4\\\\(x-\dfrac{1}{x} )^3=x^3-\dfrac{1}{x^3} -3x^2*\dfrac{1}{x}+3x*\dfrac{1}{x^2}\\\\=x^3-\dfrac{1}{x^3}-3(x-\dfrac{1}{x})\\\\x^3-\dfrac{1}{x^3}=(x-\dfrac{1}{x} )^3+3(x-\dfrac{1}{x})\\\\if\ x-\dfrac{1}{x}=4\ then \ x^3-\dfrac{1}{x^3}=4^3+3*4=64-12=76\\\\if\ x-\dfrac{1}{x}=-4\ then \ x^3-\dfrac{1}{x^3}=(-4)^3+3*(-4)=-64-12=-76\\\\$

makvit [3.9K]2 years ago

7 0

Please find attached photograph for your answer.

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3 years ago

HELP ME ASAP 20 points !!!

Molodets [167]

Mode means ‘most often number’ .

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1 year ago

How do you get the answer and sketch it to this graft

Katyanochek1 [597]

F(x) = -4(x - 2)² + 2
f(x) = -4((x - 2)(x - 2)) + 2
f(x) = -4(x² - 2x - 2x + 4) + 2
f(x) = -4(x² - 4x + 4) + 2
f(x) = -4(x²) + 4(4x) - 4(4) + 2
f(x) = -4x² + 16x - 16 + 2
f(x) = -4x² + 16x - 14
-4x² + 16x - 14 = 0
x = -16 +/- √(16² - 4(-4)(-14))
 2(-4)
x = -16 +/- √(256 - 224)
 -8
x = -16 +/- √(32)
 -8
x = -16 +/- 5.66
 -8
x = -16 + 5.66 x = -16 - 5.66
 -8 -8
x = -10.34 x = -21.66
 -8 -8
x = 1.2925 x = 2.7075
f(x) = -4x² + 16x - 14
f(1.2925) = -4(1.2925)² + 16(1.2925) - 14
f(1,2925) = -4(1.67055625) + 20.68 - 14
f(1.2925) = -6.682225 + 20.68 - 14
f(1.2925) = 13.997775 - 14
f(1.2925) = -0.002225
(x, f(x)) = (1.2925, -0.002225)
or
f(x) = -4x² + 16x - 14
f(2.7075) = -4(2.7075)² + 16(2.7075) - 14
f(2.7075) = -4(7.33055625) + 43.32 - 14
f(2.7075) = -29.322225 + 43.32 - 14
f(2.7075) = 13.997775 - 14
f(2.7075) = -0.002225
(x, f(x)) = (2.7075, -0.002225)
--------------------------------------------------------------------------------------------
f(x) = 2(x - 2)² + 1
f(x) = 2((x - 2)(x - 2)) + 1
f(x) = 2(x² - 2x - 2x + 4) + 1
f(x) = 2(x² - 4x + 4) + 1
f(x) = 2(x²) - 2(4x) + 2(4) + 1
f(x) = 2x² - 8x + 8 + 1
f(x) = 2x² - 8x + 9
2x² - 8x + 9 = 0
x = -(-8) +/- √((-8)² - 4(2)(9))
 2(2)
x = 8 +/- √(64 - 72)
 4
x = 8 +/- √(-8)
 4
x = 8 +/- √(8 × (-1))
 4
x = 8 +/- √(8)√(-1)
 4
x = 8 +/- 2.83i
 4
x = 2 +/- 1.415i
x = 2 + 1.415i x = 2 - 1.415i
f(x) = 2x² - 8x + 9
f(2 + 1.415i) = 2(2 + 1.415i)² - 8(2 + 1.415i) + 9
f(2 + 1.415i) = 2((2 + 1.415i)(2 + 1.415i)) - 16 - 11.32i + 9
f(2 + 1.415i) = 2(4 + 2.83i + 2.83i + 2.00225i²) - 16 - 11.32i + 9
f(2 + 1.415i) = 2(4 + 5.66i + 2.00225) - 16 - 11.32i + 9
f(2 + 1.415i) = 8 + 11.32i + 4.0045 - 16 - 11.32i + 9
f(2 + 1.415i) = 8 + 4.0045 - 16 + 9 + 11.32i - 11.32i
f(2 + 1.415i) = 12.0045 - 16 + 9
f(2 + 1.415i) = -3.9955 + 9
f(2 + 1.415i) = 5.0045
(x, f(x)) = (2 + 1.415i, 5.0045)
or
f(x) = 2x² - 8x + 9
f(2 - 1.415i) = 2(2 - 1.415i)² - 8(2 - 1.415i) + 9
f(2 - 1.415i) = 2((2 - 1.415i)(2 - 1.415i)) - 16 + 11.32i + 9
f(2 - 1.415i) = 2(4 - 2.83i - 2.83i + 2.00225i²) - 16 + 11.32i + 9
f(2 - 1.415i) = 2(4 - 5.66i + 2.00225) - 16 + 11.32i + 9
f(2 - 1.415i) = 8 - 11.32i + 4.0045 - 16 + 11.32i + 9
f(2 - 1.415i) = 8 + 4.0045 - 16 + 9 - 11.32i + 11.32i
f(2 - 1.415i) = 12.0045 - 16 + 9
f(2 - 1.145i) = -3.9955 + 9
f(2 - 1.415i) = 5.0045
(x, f(x)) = (2 - 1.415i, 5.0045)
--------------------------------------------------------------------------------------------
f(x) = -2(x - 4)² + 8
f(x) = -2((x - 4)(x - 4)) + 8
f(x) = -2(x² - 4x - 4x + 16) + 8
f(x) = -2(x² - 8x + 16) + 8
f(x) = -2(x²) + 2(8x) - 2(16) + 8
f(x) = -2x² + 16x - 32 + 8
f(x) = -2x² + 16x - 24
-2x² + 16x - 24 = 0
x = -16 +/- √(16² - 4(-2)(-24))
 2(-2)
x = -16 +/- √(256 - 192)
 -4
x = -16 +/- √(64)
 -4
x = -16 +/- 8
 -4
x = -16 + 8 x = -16 - 8
 -4 -4
x = -8 x = -24
 -4 -4
x = 2 x = 6
f(x) = -2x² + 16x - 24
f(2) = -2(2)² + 16(2) - 24
f(2) = -2(4) + 32 - 24
f(2) = -8 + 32 - 24
f(2) = 24 - 24
f(2) = 0
(x,f(x)) = (2, 0)
or
f(x) = -2x² + 16x - 24
f(6) = -2(6)² + 16(6) - 24
f(6) = -2(36) + 96 - 24
f(6) = -72 + 96 - 24
f(6) = 24 - 24
f(6) = 0
(x, f(x)) = (6, 0)

5 0

3 years ago

Haha once again I need the drawing

Mazyrski [523]

Answer:

hha once again i need the drawing

Step-by-step explanation:

7 0

3 years ago

M+5n=p for m Solving for a variable

Verdich [7]

Answer:

M=p-5n

Step-by-step explanation:

Here we are given that M+5n=p

We are asked to solve this equation for M. In order to do that we will follow these steps.

Subtracting 5n from both sides we get

M+5n-5n=p-5n

M=p-5n

Hence , now we have our M as dependent variable, whose value depends on the values of p and n. One or both of them can be independent variable/.

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3 years ago