Question

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If (2m + 3n) = 3 and mn = 1, what is the value of 4m2 + 9n2? 1.-3 2.-2 3.-4 4.-5

Answer 1

-3

Step-by-step explanation:

(2m + 3n) = 3

mn = 1

let 2m = a and 3m = b

therefore,

2m + 3n = a + b = 3 ---> (i)

ab = (2m×3n) = 6mn = 6(1) --->(ii)

4m² = a² and 9n² = b²

therefore,

4m² + 9n² = a²+b² = (a + b)² - 2ab ---> (iii)

substituting equations (I) & (ii) in equation (iii), we get,

4m²+9n²=(a+b)²-2ab= (3)²-2(6)=9-12= -3

therefore, 4m²-9n²= -3

Hope this helps