Question

Calculati (x²+x-1)²-2x(x-1)(x+1),daca x=$2\sqrt{7}.$

Answer 1

Folosind formule de calcul prescurtat, obtinem:
$( {x}^{2} + x - 1) ^{2} - 2x(x - 1)(x + 1) = {x}^{4} + {x}^{2} + 1 + {2x}^{3} - {2x}^{2} - 2x - 2x( {x}^{2} - 1) = {x}^{4} + 1 + {2x}^{3} - {x}^{2} - 2x - {2x}^{3} + 2x = {x}^{4} - {x}^{2} + 1.$
Acum, inlocuim pe x cu $2 \sqrt{ 7}$ si obtinem:

$(2 \sqrt{7} )^{4} - ( 2\sqrt{7} ) ^{2} + 1 = 16 \cdot 49 - 4 \cdot 7 + 1 = 784 - 28 + 1 = 757.$