Question

If 2x-3y=10,xy=8,find the value of 4x^2+ 9y^2

Answer 1

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• 2x - 3y = 10

• x.y = 8

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• To find the value of  4x² + 9y² .

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• (2x - 3y)²  =  10²
• (2x)² - 2(2x)(3y) + (3y)²  =  100    ∵ (a - b)² = a² - 2ab + b²
• 4x² - 12xy + 9y² = 100
• 4x² - 12(8) + 9y² = 100     ∵ x.y = 8 (Given)
• 4x² - 96 + 9y² = 100
• 4x² + 9y² = 100 + 96
• 4x² + 9y² = 196