Question

Compute the value of 9x2 + 4y2 if xy = 6 and 3x + 2y = 12​

Answer 1

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

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Answer 2

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.