Compute the value of 9x2 + 4y2 if xy = 6 and 3x + 2y = 12
Answers
Answered by
82
Step-by-step explanation:
9x²+4y²
= (3x)²+(2y)²
= (3x+2y)²-2.3x.2y
= (3x+2y)²-12xy
= (12)²-12×6
= 144-72
= 72
Read my bio only once please
Answered by
71
Given:
Two equations, 3x + 2y = 12 and x*y =6.
To Find:
The value of 9x²+4y² using the above equations.
Solution:
The given problem can be solved using the expansion of (a+b)².
1. The given equations are 3x + 2y = 12 and x*y =6,
2. Consider the equation 3x + 2y = 12,
=> Apply sqaure on both the sides of the equation,
=> (3x+2y)² = (12)²,
=> 9x² + 4y² + 12xy = 144, ( Using the expansion (a+b)² = a² + b² +2ab)
=> 9x² + 4y² = 144 - 12xy,
=> 9x² + 4y² = 144 - 12(6) (As xy = 6),
=> 9x² + 4y² = 144 - 72,
=> 9x² + 4y² = 72.
Therefore, the value of 9x² + 4y² is 72.
Similar questions