Question

11. determinati x apartine r din proportiile
a)13/x=x/13
b)5x/4=20
c)3-x^2/16=1/8
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Answer 1

Răspuns:

a) x = ±13

b) x = 16

c) x = ±1

Explicație pas cu pas:

a) $\frac{13}{x} = \frac{x}{13}$  ⇒ x² = 13² ⇒ x = ±13

b) $\frac{5x}{4} = 20$ ⇒ 5x = 80 ⇒ x = 80:5 ⇒ x = 16

c) $\frac{3-x^{2} }{16} = \frac{1}{8}$  ⇒  24 - 8x² = 16 ⇒ 8x² = 24-16 ⇒ 8x² = 8 ⇒ x² = 1 ⇒ x = ±1

Answer 2

a) 13/x=x/13

x²=169 => x1=+13, x2=-13

b) 5x/4=20

5x=20×4

5x=80 => x=16

c) 3-x²/16=1/8

(3-x²)×8=16

-8x²+24=16

-8x²+8=0 /÷8

-x²+1=0

-x²=-1

x²=1 => x1=1, x2=-1