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3 years ago

What are the solutions to the system of equations? {y=2x²−6x+3 {y=x−2

Mathematics

1 answer:

katrin2010 [14]3 years ago

3 0

Answer:

x = 1, y = −1

x = 5/2, y = 1/2

Step-by-step explanation:

From the question given above, the following data were obtained:

y = 2x² − 6x + 3 ........ (1)

y = x − 2 ...... (2)

We can obtain the solutions to the equation as follow:

y = 2x² − 6x + 3 ........ (1)

y = x − 2 ...... (2)

Substitute the value of y in equation 2 into equation 1

y = 2x² − 6x + 3

y = x − 2

2x² − 6x + 3 = x − 2

Rearrange

2x² − 6x − x + 3 + 2 = 0

2x² − 7x + 5 = 0

Solve by factorization

Obtain the product of 2x² and 5. The result is 10x².

Find two factors of 10x² such that their sum will result to −7x.

The factors are −2x and −5x.

Replace −7x in the equation above with −2x and −5x as shown below:

2x² − 2x − 5x + 5 = 0

2x(x − 1) − 5(x − 1) = 0

(x − 1)(2x − 5) = 0

x − 1 = 0 or 2x − 5 = 0

x = 1 or 2x = 5

x = 1 or x = 5/2

Substitute the value of x into equation 2 to obtain y

y = x − 2

x = 1

y = 1 − 2

y = −1

x = 5/2

y = x − 2

y = 5/2 − 2

y = (5 − 4)/2

y = 1/2

SUMMARY:

x = 1, y = −1

x = 5/2, y = 1/2

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The product is $104 x^{4}+16 \sqrt{30} x^{4}$

Explanation:

The given expression is $\left(4 x \sqrt{5 x^{2}}+2 x^{2} \sqrt{6}\right)^{2}$

We need to determine the product of the given expression.

First, we shall simplify the given expression.

Thus, we have,

$\left(4 x \sqrt{5 x^{2}}+2 x^{2} \sqrt{6}\right)^{2}=\left(4 x \sqrt{5} x+2 x^{2} \sqrt{6}\right)^2$

$\left(4 x \sqrt{5 x^{2}}+2 x^{2} \sqrt{6}\right)^{2}=\left(4 x^{2} \sqrt{5}+2 x^{2} \sqrt{6}\right)^2$

Expanding the expression, we have,

$\left(4 x \sqrt{5 x^{2}}+2 x^{2} \sqrt{6}\right)^{2}=\left(4 x^{2} \sqrt{5}+2 x^{2} \sqrt{6}\right)\left(4 x^{2} \sqrt{5}+2 x^{2} \sqrt{6}\right)$

Now, we shall apply FOIL, we get,

$\left(4 x \sqrt{5 x^{2}}+2 x^{2} \sqrt{6}\right)^{2}=\left(4 x^{2} \sqrt{5}\right)^{2}+2 ( 2 x^{2} \sqrt{6})(4 x^{2} \sqrt{5})+\left(2 x^{2} \sqrt{6}\right)^{2}$

Simplifying the terms, we have,

$\left(4 x \sqrt{5 x^{2}}+2 x^{2} \sqrt{6}\right)^{2}=16 \cdot 5 x^{4}+16 \sqrt{30} x^{4}+4 \cdot 6 x^{4}$

Multiplying, we get,

$\left(4 x \sqrt{5 x^{2}}+2 x^{2} \sqrt{6}\right)^{2}=80 x^{4}+16 \sqrt{30} x^{4}+24 x^{4}$

Adding the like terms, we get,

$\left(4 x \sqrt{5 x^{2}}+2 x^{2} \sqrt{6}\right)^{2}=104 x^{4}+16 \sqrt{30} x^{4}$

Thus, the product of the given expression is $104 x^{4}+16 \sqrt{30} x^{4}$

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