Question

2. If 3x + 2y =15 and xy = 8 find the value of 9xpower2+ 4ypower2​

Answer 1

Given:-

• if 3x + 2y = 15 and xy = 8

To Find:-

• The value of 9x² + 4y²

FORMULAE USED:-

• (x + y)² = x² + y² +2xy

Now,

→ 3x + 2y = 15

• Squaring the both sides.

→ (3x + 2y)² = 3x² + 2y² + 2 × 3x × 2y

→ (15)² = 9x² + 4y² + 12xy

→ 225 = 9x² + 4y² + 12× 8

→ 225 = 9x² + 4y² + 96

→ 225 - 96 = 9x² + 4y²

→ 129 = 9x² + 4y².

Hence, The value of 9x² + 4y² is 129.

MORE IDENTITIES

• (a - b)² = a² - 2ab + b²

• a³ + b³ = (a + b ) (a² - ab + b²)

• a³ - b³ = (a - b ) (a² + ab + b²).

Answer 2

Answer:

$\small\bold{\underline{\sf{\purple{Given:-}}}}$

if 3x + 2y = 15 and xy = 8

$\small\bold{\underline{\sf{\red{To\:Find:-}}}}$

The value of 9x² + 4y²

$\small\bold{\underline{\sf{\pink{Formula\:used:-}}}}$

(x + y)² = x² + y² +2xy

Now,

→ 3x + 2y = 15

Squaring the both sides.

→ (3x + 2y)² = 3x² + 2y² + 2 × 3x × 2y

→ (15)² = 9x² + 4y² + 12xy

→ 225 = 9x² + 4y² + 12× 8

→ 225 = 9x² + 4y² + 96

→ 225 - 96 = 9x² + 4y²

→ 129 = 9x² + 4y².

Hence, The value of 9x² + 4y² is 129.