Question

Exercițiul 6! Determinati x = R, din ecuațiile:
(Aveți exercițiul in imagine), Dau 50 puncte + coroana!

Answer 1

Explicație pas cu pas:

a)

${x}^{2} = 16 \times 25 = {4}^{2} \times {5}^{2} = {(4 \times 5)}^{2} = {20}^{2}$

$|x| = 20 \implies x = \pm 20$

b)

$\dfrac{x^{2} }{100} = \dfrac{1}{64} \iff {x}^{2} = \dfrac{100}{64} = \dfrac{ {10}^{2} }{ {8}^{2} } = {\bigg(\dfrac{10}{8}\bigg)}^{2} = {\bigg(\dfrac{5}{4}\bigg)}^{2}$

$|x| = \dfrac{5}{4} \implies x = \pm \dfrac{5}{4}$

c)

$\dfrac{x^{2} }{25} = \dfrac{36}{100} \iff {x}^{2} = \dfrac{25 \times 36}{100} = 9 = {3}^{2}$

$|x| = 3 \implies x = \pm 3$

d)

$36 {x}^{2} - 25 = 0 \iff {x}^{2} = \dfrac{25}{36} = \dfrac{ {5}^{2} }{ {6}^{2} } = {\bigg(\dfrac{5}{6}\bigg)}^{2}$

$|x| = \dfrac{5}{6} \implies x = \pm \dfrac{5}{6}$