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2 years ago

If x+2y=3 and xy=2 show that x³+8y³+9=0

Mathematics

1 answer:

kicyunya [14]2 years ago

4 0

Step-by-step explanation:

<u>Given</u>

x + 2y = 3 and xy = 2
show that x³ + 8y³ + 9 = 0

<u>Solution in steps:</u>

(x + 2y)³ = 3³
x³ + 3x²(2y) + 3x(2y)² + (2y)³ = 27
x³ + 6x(xy) + 12y(xy) + 8y³ = 27
x³ + 8y³ + 6(x + 2y)xy = 27 ⇒ Substitute values
x³ + 8y³ + 6*3*2 = 27
x³ + 8y³ + 36 - 27 = 0
x³ + 8y³ + 9 = 0

Done

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3 years ago

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The equations represent the line that is parallel to 3x - 4y = 7 and pass through the point (-4,-2) are:

$y+2=\frac{3}{4}\left(x+4\right)$

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Step-by-step explanation:

The slope-intercept form of the line equation

$y = mx+b$

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b is the y-intercept

Given the line

3x - 4y = 7

writing in the slope-intercept form

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dividing both sides by 4

4y/4 = 3/4x - 7/4

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Now, comparing with the slope-intercept form of the line equation

y = 3/4x - 7/4

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We know that parallel lines have the same slopes.

Therefore, the slope of the parallel line is: 3/4

now we have,

The point (-4, -2)

The slope m of parallel line = 3/4

Given the point-slope form of the line equation

$y-y_1=m\left(x-x_1\right)$

where m is the slope of the line and (x₁, y₁) is the point

substituting (-4, -2) and m = 3/4 in the point-slope form of line equation

$\:y-\left(-2\right)=\frac{3}{4}\left(x-\left(-4\right)\right)$

$y+2=\frac{3}{4}\left(x+4\right)$

Thus, the equation in the point-slope form of the line equation is:

$y+2=\frac{3}{4}\left(x+4\right)$

Simplifying the equation

$y+2=\frac{3}{4}\left(x+4\right)$

Subtract 3 from both sides

$y+2-2=\frac{3}{4}\left(x+4\right)-2$

$y=\frac{3}{4}x+1$

Multiplying the equation by 4

$4y = 3x + 4$

$3x - 4y = -4$

Therefore, the equations represent the line that is parallel to 3x - 4y = 7 and pass through the point (-4,-2) are:

$y+2=\frac{3}{4}\left(x+4\right)$

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3 years ago

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Answer:

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Step-by-step explanation:

R ∝ S/ T

》R = kS/ T

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then, k = (8 × 3)/ 4

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3 years ago

If x+2y=3 and xy=2 show that x³+8y³+9=0​

If x+2y=3 and xy=2 show that x³+8y³+9=0