Question

If 9x^2 + 4y^2 = 57 and xy = 2 then, find the value of 3x + 2y.

Answer 1

Step-by-step explanation:

#. if 9x^2 + 4y^2 = 52:

Substitute X and y = 2 in 9(2)^2+4(2)^2 = 52

36+16 = 52

#.Then substitute the value for x and y = 2 in 3x + 2y

3(2) + 2(2) = ?

6 + 4 = 10

Therefore the values of 3x and 2x is 10

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Answer 2

Answer:

The value of 3x + 2y is 9.

Step-by-step explanation:

Given,

$9 {x}^{2} + 4 {y}^{2} = 57$

${(3x)}^{2} + {(2y)}^{2} = 57$

${(3x + 2y)}^{2} - 2 \times 3x \times 2y = 57 \\ {(3x + 2y)}^{2} - 12xy = 57$

Given,xy=2

So,

${(3x + 2y)}^{2} - 12xy = 57 \\ {(3x + 2y)}^{2} - 12 \times 2 = 57 \\ {(3x + 2y)}^{2} - 24 = 57 \\ {(3x + 2y)}^{2} = 57 + 24 \\ {(3x + 2y)}^{2} = 81 \\ (3x + 2y) = \sqrt{81} \\ (3x + 2y) = 9$

Required value of (3x + 2y) is 9.

This is a problem of Algebra.

Some important Algebra formulas.

(a + b)² = a² + 2ab + b²

(a − b)² = a² − 2ab − b²

(a + b)³ = a³ + 3a²b + 3ab² + b³

(a - b)³ = a³ - 3a²b + 3ab² - b³

a³ + b³ = (a + b)³ − 3ab(a + b)

a³ - b³ = (a -b)³ + 3ab(a - b)

a² − b² = (a + b)(a − b)

a² + b² = (a + b)² − 2ab

a² + b² = (a − b)² + 2ab

a³ − b³ = (a − b)(a² + ab + b²)

a³ + b³ = (a + b)(a² − ab + b²)

Know more about Algebra,

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