Question

Cho x² - y² = 1. Tính giá trị biểu thức A = 2 ( x⁶ - y⁶ ) - 3 ( x⁴ + y⁴ ).

Answer 1

\(A=2\left(x^6-y^6\right)-3\left(x^4+y^4\right)\)

\(A=2\left(x^2-y^2\right)\left(x^4+x^2y^2+y^4\right)-3\left(x^4+y^4\right)\)

\(A=2\left(x^4+x^2y^2+y^4\right)-3\left(x^4+y^4\right)\)

\(A=2x^4+2x^2y^2+2y^4-3x^4-3y^4\)

\(A=-\left(x^4-2x^2y^2+y^4\right)\)

\(A=-\left(x^2-y^2\right)^2=-1^2=-1\)

Vậy A=-1

Answer 2

\(A=2\left(x^6-y^6\right)-3\left(x^4+y^4+y^4\right)\)