Question

If 2x + 3y =10 and xy 5, find the value of 4x + 9y. Also, find the value of 2x+3y when xy=2

Answer 1

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

$\huge{\bf{Solution:-}}$

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)