Question

If 2x + 3y = 10 and xy = 5; find the value of 4x² + 9y²

Answer 1

Given 2x + 3y = 10 and xy = 5
4x² +9y²
= (2x²) + (3y)²
= (2x + 3y)² - 2(2x)(3y)   
......[∵ (a + b)² + a² + b² + 2ab, so, a² + b² = (a + b)² - 2ab]
= (10)²  - 12(5)
= 100 - 60
= 40.