Question

What's the answer? help asap
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Answer 1

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Given,

`3x - 2y = 5`

`xy = - 2`

Now,

`(3x - 2y) {}^(2) = (5) {}^(2) \\`

Use the algebraic identity ⇻ (a - b)² = a² - 2ab + b²

`(3x - 2y) {}^(2) = (5) {}^(2) \\ 3x {}^(2) - 2 * 3x * 2y + 2y {}^(2) = 5 {}^(2) \\ 9 {x}^(2) - 12xy + 4y {}^(2) = 25 \\9x {}^(2) + 4y {}^(2) = 25 + 12xy \\ 9x {}^(2) + 4 {y}^(2) - 1 = 24 + 12xy`

✐ So, the value of 9x² + 4y² - 1 is 24 + 12xy

Now,

xy = - 2

So, 12xy = 12 × - 2 = - 24

•°• 24 + 12xy

= 24 + (-24)

= 24 - 24

= 0

⎆ The value of 9x² + 4y² - 1 is 0.

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