Question

Aflati doua numere care inmultite dau 144 iar suma lor este 25.

Answer 1

Răspuns:

xy=144

x+y=25 =>x=25-y

(25-y)y=144

25y - y^2 = 144

-y^2 + 25y - 144 = 0

y^2 - 25y + 144 = 0

delta = 625 - 4×144 = 625 - 576 = 49 => rad.delta = 7

y1=(25-7)/2=9 =>x1=16

y2=(25+7)/2=16 =>x2=9

Answer 2

Răspuns:

$S = \Bigg\{(9,16); (16, 9)\Bigg\}$

Explicație pas cu pas:

$\begin{cases}a\cdot b = 144\\a+b = 25\end{cases}\\\\ a+b = 25 \iff a = 25 - b\\\\ a\cdot b = 144\iff (25-b) \cdot b = 144\\\\ 25b - b^2 = 144\\\\ b^2 - 25b + 144 = 0\\\\ \Delta = 625 - 4\cdot 144 = 625 - 576 = 49 \implies \sqrt{\Delta} = 7\\\\ b_{1,2} = \frac{25\pm 7}{2}\\\\ b_1 = 16\\\\ b_2 = 9\\\\ b = 16\iff a = 9\\\\ b = 9 \iff a = 16\\\\ S = \Bigg\{(9,16); (16, 9)\Bigg\}$