Question

Нехай х1 та х2-корені квадратного рiвняння х² - 9x + 8 = 0. Обчисліть x² + x2​

Answer 1

Відповідь:

x^2 - 9x +8 = 0

D = 81 - 4 * 1  * 8 = 81 -32 = 49

x1 = 9 + 7 /2 = 16/2 = 8

x2 = 9-7 / 2 =2/2 = 1

x1^2 + x2^2 = 8^2 + 1^2 = 64 + 1 = 65

Answer 2

$\displaystyle\bf\\x^{2} -9x+8=0\\\\Teorema \ Vieta \ : \ \\\\x_{1} + x_{2} =9\\\\x_{1} \cdot x_{2} =8\\\\\\\Big(\underbrace{x_{1} + x_{2} }_{9}\Big)^{2} =x_{1} ^{2} +2\cdot \underbrace{x_{1} \cdot x_{2}}_{8} +x_{2} ^{2} \\\\\\81=x_{1} ^{2} +16+x_{2} ^{2} \\\\x_{1} ^{2} +x_{2} ^{2} =81-16\\\\\boxed{x_{1} ^{2} +x_{2} ^{2} =65}$