If 2x +3y = 8 and xy = 2, find the value of 4x² +9y²
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Given : 2x + 3y = 8 and xy = 2, To find : value of 4x² + 9y²
Solution :
By using an identity (a + b)² = a² + b² + 2ab
On Squaring 2x + 3y = 8 both sides we get :
(2x + 3y)² = 8²
(2x)² + (3y)² + 2 × 2x × 3y = 64
4x² + 9y² + 12xy = 64
4x² + 9y² + 12(2) = 64
[xy = 2]
4x² + 9y² + 24 = 64
4x² + 9y² = 64 - 24
4x² + 9y² = 40
Hence the value of 4x² + 9y² is 40.
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