bonjour
[x ( 8 - x ) ] / 2 = [8 x - x² ] / 2 = 4 x - 0.5 x ²
aire AGH = - 0.5 x² + 4 x
8 - 1/2 ( x - 4 ) ²
= 8 - 1 /2 ( x² - 8 x + 16 )
= 8 - x²/2 + 8 x /2 - 16 /2
= 8 - 0.5 x² + 4 x - 8
= - 0.5 x² + 4 x
aire des 4 triangles = 4 ( - 0.5 x² + 4 x ) = - 2 x² + 16 x
aire mauve = 8 ² - ( - 2 x² + 16 x )
= 64 + 2 x² - 16 x
2 x² - 16 x + 64 = 32
2 x² - 16 x + 64 - 32 = 0
2 x² - 16 x + 32 = 0
Δ = 256 - 4 ( 2 * 32 ) = 256 - 256 = 0
Δ = 0 donc 1 seule solution x ₀ = 16/4 = 4