Question

12) If 4x – 3y =10 and xy=-1, then find the value of 16x2 +9y2.​

Answer 1

Answer:

Step-by-step explanation:

Correct Question :--- If 2x + 3y =10 and xy 5, find the value of 4x² + 9y² ...

Solution :---

→ 2x + 3y = 10

Squaring both sides we get,

→ (2x + 3y)² = (10)²

Using (a+b)² = a² + b² + 2ab now, we get,

→ 4x² + 9y² + 2*2x*3y = 100

→ 4x² + 9y² + 12xy = 100

Putting value of xy = 5 now,

→ 4x² + 9y² + 12*5 = 100

→ 4x² + 9y² + 60 = 100

→ 4x² + 9y² = 100 - 60

→ 4x² + 9y² = 40 (Ans)..

______________________________

we also have to Find value of (2x+3y) when xy = 2 .

we have now, = 4x² + 9y² = 40

→ 4x² + 9y² = 40

Adding 12xy both sides we get,

→ 4x² + 9y² + 12xy = 40 + 12xy

Putting value of xy in RHS we get,

→ 4x² + 9y² + 12xy = 40 + 12*2

→ 4x² + 9y² + 12xy = 64

→ (2x+3y)² = 64

Square root both sides now we get,

→ (2x+3y) = ± 8 .

Hence, value of (2x+3y) will be 8 or (-8) when xy is 2.

Answer 2

Answer:

Required value of $16 {x}^{2} + 9 {y}^{2}$ is 76

Step-by-step explanation:

Given,

$4x - 3y = 10...(1)$ and $xy = - 1$

Here we want to find value of

$16 {x}^{2} + 9 {y}^{2}$

So,

$16 {x}^{2} + 9 {y}^{2} \\ = {(4x)}^{2} + {(3y)}^{2} \\ = {(4x - 3y)}^{2} + 2.4x.3y \\ = {(4x - 3y)}^{2} + 24xy \\ = {10}^{2} + 24 \times ( - 1) \\ = 100 - 24 \\ = 76$

Here applied formula,

${a}^{2} + {b}^{2} = {(a - b)}^{2} + 2ab$

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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2) https://brainly.in/question/1169549