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Math Question 2

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Subject

Mathematics

Type

Homework

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creary0999

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In order to solve this problem, you have to understand these concepts: factoring

polynomials, using the FOIL method in multiplying binomials and determining possible

factors of real numbers.

Given: x

+ 4y

= 40

xy = 6

Required: Value of x + 2y

Solution:

In order to get the value of "x + 2y", solve for the values of "x" and "y". Since there are

two equations given and two unknown variables, it is possible to determine the values of

"x" and "y".

Step 1: Using the equation "xy=6", solve for the value of "y" in terms of "x" by dividing

both sides of the equation by "x"

(xy)/x = 6/x

y=6/x

Step 2: Using the equation "x

+ 4y

= 40", substitute "y=6/x". Resulting equation would

be:

+ 4(6/x)

= 40

Step 3: Expand the equation

+ 4(6

/ x

) = 40

+ 4(36 / x

) = 40

+ (144 / x

) = 40

Step 4: Simplify the equation by removing fractions. In this case we have to remove "x

by multiplying both sides of the equation by "x

) [x

+ (144 / x

)] = (40) (x

)

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+ 144 = 40x

Step 5: Place all parts of the equation on one side, then arrange every term from

highest to lowest degree of exponents to easily factor the polynomial

- 40x

+144 = 0

The resulting polynomial is a 4th degree polynomial. To simplify things,

Let u = x

, resulting equation would be

- 40u +144 = 0 (I simply used "u" to represent "x

" in order to easily factor the

polynomial)

Step 6: Factor "u

- 40u +144 = 0"

Remember the FOIL (FIRST, OUTSIDE, INSIDE, LAST) Method: (x+a)(x+b) = x

+ bx +

ax + ab

By reversing the FOIL Method, you'll come up with 2 factors.

In our equation: u

- 40u +144 = 0

Look for factors of "u

", then look for possible factors of "+144" that would result to "-40"

when added. Resulting factors would be "-36" and "-4"

Reversing the FOIL Method would give us:

(u-36)(u-4) = 0

Step 7: Find the values of "u" using zero product rule. When ab=0, a=0 / b=0, therefore

we can equate both factors by 0 in order to get the values of "u"

u-36=0 ; u-4=0

u=36 u=4

Step 8: Remember that "u = x

", therefore

= 36; x = +6 and -6

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In order to solve this problem, you have to understand these concepts: factoring polynomials, using the FOIL method in multiplying binomials and determining possible factors of real numbers. Given: x2 + 4y2 = 40 xy = 6 Required: Value of x + 2y Solution: In order to get the value of "x + 2y", solve for the values of "x" and "y". Since there are two equations given and two unknown variables, it is possible to determine the values of "x" and "y". Step 1: Using the equation "xy=6", solve for the value of "y" in terms of "x" by dividing both sides of the equation by "x" (xy)/x = 6/x y=6/x Step 2: Using the equation "x2 + 4y2 = 40", substitute "y=6/x". Resulting equation would be: x2 + 4(6/x)2 = 40 Step 3: Expand the equation x2 + 4(62 / x2) = 40 x2 + 4(36 / x2) = 40 x2 + (144 / x2) = 40 Step 4: Simplify the equation by removing fractions. In this case we have to remove "x2" by multiplying both sides of the equation by "x2" (x2) [x2 + (144 / x2)] = (40) (x2) x4 + 144 = 40x2 Step 5: Place all parts of the equation on one side, then arrange every term from highest to lowest degree of exponents to easily factor the polynomial x4 - 40x2 +144 = 0 The resulting polynomial is a 4th degree polynomial. To simplify things, Let u = x2, resulting equation would be u2 - 40u +144 = 0 (I simply used "u" to represent "x2" in order to easily factor the polynomial) Step 6: Factor "u2 - 40u +144 = 0" Remember the FOIL (FIRST, OUTSIDE, INSIDE, LAST) Method: (x+a)(x+b) = x2 + bx + ax + ab By reversi ...
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