Question

If 2x + 3y = 14 and 2x - 3y = 2, find the value of xy.
[Hint: Use (2x + 3y)2 - (2x - 3y)2 = 24xy]​

Answer 1

Solution:

Given –

→ 2x + 3y = 14 — (i)

→ 2x - 3y = 2 — (ii)

• We have to find out the value of x and y.

There are two ways to solve this problem.

Process 1.

Squaring both sides of (i), we get,

→ (2x + 3y)² = 14²

→ 4x² + 9y² + 12xy = 196 — (iii)

Squaring both sides of (ii), we get,

→ 4x² + 9y² - 12xy = 4 — (iv)

Subtracting (iv) from (iii), we get,

→ 24xy = 192

→ xy = 8

So, xy = 8 ★

Process 2.

Adding (i) and (ii), we get,

→ 4x = 16

→ x = 4

Substituting the value of x in (i), we get,

→ 2 × 4 + 3 × y = 14

→ 3y = 14 - 8

→ 3y = 6

→ y = 2

So,

→ x = 4 and y = 2

Therefore,

→ xy = 4 × 2 = 8 ★

Answer:

• The value of xy is 8.

Learn More:

• Some identities.

• (a + b)² = a² + 2ab + b²
• (a - b)² = a² - 2ab + b²
• a² - b² = (a + b)(a - b)
• (a + b)³ = a³ + 3ab(a + b) + b³
• (a - b)³ = a³ - 3ab(a - b) - b³
• a³ + b³ = (a + b)(a² - ab + b²)
• a³ - b³ = (a - b)(a² + ab + b²)