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Inequality Value Of X And Y

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Inequality Value of X and Y

If x²+4y²=40 and xy=6, what will be the value of x+2y? Please explain how you arrived

at your answer.

X

2

+ 4Y

2

= 40 … (1) and XY=6… (2). Make X the subject of the equation in 2.

Hence, X=6/Y… (3). Substitute equation (3) in equation (1), we obtain (6/Y)

2

+ 4Y

2

=

40… (4)

Solve for Y in equation (4), 36/Y

2

+ 4Y

2

= 40. To substitute for the Y

2

in the

denominator, we multiply both sides of the equation with the value Y

2

. (36/Y

2

) *Y

2

+ (4Y

2

* Y

2

)

= (40 * Y

2

). After multiplying we get the following equation, 36 + 4Y

4

= 40Y

2

. Given that all the

values are multiples of 4, we divide all through with 4. 36/4 + 4Y

4

/4 = 40Y

2

/4 which gives us 9

+ Y

4

= 10Y

2

. Make the equation to quadratic form as in the formulae ax

2

+ bx + c = 0, which is

Y

4

- 10Y

2

+ 9 = 0. Solve the equation using the quadratic formula y=(−b±√b2−4ac)/2a.

Where a = 1, b = -10 and C = 9. Therefore, Y

2

= {-(-10) ±√(-10

2

) – (4*1*9)}/ (2*1)

Y

2

= {10 ±√(100) – (36)}/2, Y

2

= (10 ±√64)/2, Y

2

= (10±8)/2, Y

2

= 2/2,18/2. Therefore,

Y

2

= 1 or 9. Square root of Y

2

we get Y = 1 or 3. Hence, Substituting Y in equation 3, we obtain

X= 6/1 (when Y = 1) and X = 6/3 (when Y = 3). So, X = 6 or 2. Hence, the values of X and Y

are; when Y = 1, X = 6, and when Y = 3, X = 2.

To obtain the value of X + 2Y, we substitute the values of X and Y in the equation.

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Surname: 1 Name: Tutor’s Name: Course: Date: Inequality Value of X and Y If x²+4y²=40 and xy=6, what will be the value of x+2y? Please explain how you arrived at your answer. X2 + 4Y2 = 40 … (1) and XY=6… (2). Make X the subject of the equation in 2. Hence, X=6/Y… (3). Substitute equation (3) in equation (1), we obtain (6/Y)2 + 4Y2 = 40… (4) Solve for Y in equation (4), 36/Y2 + 4Y2 = 40. To substitute for the Y2 in the denominator, we multiply both sides of the equation with the value Y2. (36/Y2) *Y2 + (4Y2 * Y2) = (40 * Y2). After multiplying we get the following equation, 36 + 4 ...
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