2. If 3x + 2y = 12 and xy = 6, find the value of 9x2 + 4y2.

Problem Analysis: Given equations: 3x+2y=123x+2y=12 xy=6xy=6 We need to find the value of 9x2+4y29x2+4y2. Solution: Step 1: Find the values of xx and yy To solve the system of equations, we can use substitution or elimination method. From equation (2), xy=6xy=6, we can express yy in terms of xx: y=6xy=x6 Substitute this expression for yy into equation (1): 3x+2(6x)=123x+2(x6)=12 Now solve for xx: 3x+12x=123x+x12=12 3x2+12=12x3x2+12=12x 3x2−12x+12=03x2−12x+12=0 Divide the equation by 3: x2−4x+4=0x2−4x+4=0 Factorize: (x−2)2=0(x−2)2=0 So, x=2x=2. Now, substitute x=2x=2 into equation (2) to find yy: 2y=62y=6 y=3y=3 So, x=2x=2 and y=3y=3. Step 2: Find the value of 9x2+4y29x2+4y2 Substitute the values of xx and yy into the expression 9x2+4y29x2+4y2: 9(2)2+4(3)29(2)2+4(3)2 9(4)+4(9)9(4)+4(9) 36+3636+36 7272 Conclusion: The value of 9x2+4y29x2+4y2 is 7272. read less