Question

a²·b²=? in functie de a+b si a·b

Answer 1

Răspuns:

$a^2\cdot b^2 =\dfrac{\big[(a+b)^2-2ab\big]^2- \big[(a+b)^2-4ab\big](a+b)^2}{4}$

Explicație pas cu pas:

(a²+b²)² = a⁴ + b⁴ + 2a²b²

[(a+b)²-2ab]² = (a²-b²)² + 2a²b² + 2a²b²

[(a+b)²-2ab]² = (a²-b²)² + 4a²b²

[(a+b)²-2ab]² = (a-b)²(a+b)² + 4a²b²

[(a+b)²-2ab]² = (a²-2ab+b²)(a+b)² + 4a²b²

[(a+b)²-2ab]² = [(a+b)²-4ab](a+b)² + 4a²b²

4a²b² = [(a+b)²-2ab]² - [(a+b)²-4ab](a+b)²

$\Rightarrow a^2\cdot b^2 =\dfrac{\big[(a+b)^2-2ab\big]^2- \big[(a+b)^2-4ab\big](a+b)^2}{4}$