Question

знайди значення виразу x ^ 2 + 9/х ^ 2 якщо x + 3/x = 5
даю 15​

Answer 1

Ответ:

19

Объяснение:

$25 = 5^2 = (x + 3/x)^2 = x^2 + 2*x*3/x + (3/x)^2 = x^2 + 6 + 9/x^2 = (x^2 + 9/x^2) + 6\\\\x^2 + 9/x^2 = 25 - 6 = 19$

Answer 2

$\displaystyle\bf\\x+\frac{3}{x} =5\\\\\\\Big(x+\frac{3}{x} \Big)^{2} =5^{2} \\\\\\x^{2} +2\cdot x\cdot \frac{3}{x} +\Big(\frac{3}{x} \Big)^{2} =25\\\\\\x^{2} +6+\frac{9}{x^{2} }=25\\\\\\x^{2} +\frac{9}{x^{2} }=25-6\\\\\\\boxed{x^{2} +\frac{9}{x^{2} }=19}$