If 3x + 2y =15 and xy = 8 find the value of 9xpower2+ 4ypower2
Answers
if 3x + 2y = 15 and xy = 8
The value of 9x² + 4y²
(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.
Step-by-step explanation:
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).